Special Factorization
177 videos • 3,835 views • by Ms Shaws Math Class
1
Simplify expression sqrt(4x +1 - 4sqrt(x)) + |sqrt(x) -1| when x is in interval (1/4, 1)
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2
For real number a, x = a^2 +1/a^2, express sqrt(x+2) - sqrt(x-2) as a polynomial in a.
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3
When a is decimal part of sqrt(5), find value of sqrt(a -1/2)^2) + sqrt(a - 1/5)^2).
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4
Given three polynomials, x^2 -1, x^2 -6x +5, x^2 +3x +3a, the GCF is degree of 1. Find value of a
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5
When polynomial P(x) = x^3 +ax^2 +bx -2 is divided by x+2 and x-1 with no remainders. Find a^2 - b^2
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6
For triangle with lengths a, b, c evaluate triangle a^3 + b^3 + c^3 = 3abc using Advanced Factoring
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7
If a is integer and b is decimal part of sqrt(11+ sqrt(72)) evaluate sqrt(b+1 + sqrt(b^2 +2b))
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8
If a is integer and b is decimal part of sqrt(11+ sqrt(72)) evaluate sqrt(b+1 + sqrt(b^2 +2b))
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9
When a is integer and b is decimal part of irrational sqrt(11 + sqrt(72)), evaluate a + 1/(b-1).
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10
Find remainder when polynomial is divided by (x-1)(x-2)(x-3). Remainder is 1 when divided by (x-1).
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11
Evaluate triangle a^3 -ac^2 + a^2b - bc^2 =0 with sides a, b, c. Determine type of triangle
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12
Evaluate expression using factoring (1 - 1/2^2)(1 - 1/3^2)(1- 1/4^2)……(1 - 1/99^2)(1- 1/100^2).
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13
Evaluate expression using factoring 3(2^2 +1)(2^4 +1)(2^8 +1) +1.
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14
Evaluate expression using factoring (99*101 + 99*2)/(101^2 -4).
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15
Evaluate each expression using factoring 25^2 + 30*25 + 15^2 and 65^2 -2*65*35 + 35^2.
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16
Evaluate expression using factoring (1000^3 +1)/(1000^2 -999).
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17
Evaluate expression using factoring (3+1)(3^2 +1)(3^4 +1)(3^8 +1).
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18
Evaluate expression using factoring (97/100)^3 + (3/100)^3 -1.
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19
Simplify expression sqrt(4+ sqrt(7)) - sqrt(4 - sqrt(7)). Advanced Factoring
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20
Simplify expression sqrt(9+ sqrt(72)) - sqrt(9 - sqrt(72)). Advanced Factoring
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21
Evaluate expression x^3 +1/x^3 when x = sqrt(3 + sqrt(8)). Advanced Factoring
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22
Evaluate expression (sqrt(x) - sqrt(y))/(sqrt(x) + sqrt(y)) when x = sqrt(5+ 2 sqrt(6)).
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23
Evaluate expression when x = sqrt(2). 1/sqrt(x +1 + 2 sqrt(x)) - 1/(sqrt(x +1 -2 sqrt(x)). Factoring
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24
Simplify expression 1- 1/(1 - 1/(1-x)). Complex Rational
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25
Simplify expression 1-(x-y)/(x+y)/1 + (x-y)/(x+y). Complex Rational
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26
Find value of abc (real numbers) when a+b+c =sqrt(3) and a^2 + b^2 + c^2 = 1. Advanced Factoring
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27
When x+y+z=1, factor polynomial x^2 -3xy +2y^2 -4x -y -2z -1. Advanced Factoring
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28
Find value of k to make polynomials perfect square trinomial. X^2 + 5x +k and 9x^2 -12x + k.
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29
Find value of k to make polynomials perfect square trinomial. 2x^2 -6x +k and 25x^2 +4x +k
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30
Find value of k to make polynomials perfect square trinomial. 4x^2 -kx +25 and 1/25 x^2 +kx + 4
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31
Find value of k to make polynomials perfect square. 9x^2 + (2k-4)x +4, 2x^2 +kx+8
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32
Find value of x to make polynomials perfect square. 4x^2+(k+5)x +9y^2, k-1/4 xy + 1/4 y^2.
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33
Evaluate each expression using factorization, 99^2 -1, 99^2 - 89^2, 49^2 - 51^2.
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34
Evaluate each expression using factorization, 3^8 -1 and 6^2 - 5^2 + 4^2 -3^2 +2^2 -1.
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35
Find value of a+b for equation (2x^2 y^3)^a divided by 4xy times 1/2 x^2 y = bx^3 y^3
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36
Two polynomials are equal find x, y, z, f(x) = (k^2 +k)x -(k^2 -k)y + (k-1)z. Equate coefficients.
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37
Two polynomials equal f(x) = g(x), find a, b, c when f(x) = a(x-1)(x-2) +b(x-2)(x-3) +c(x-3)(x-1)
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38
For real number a, evaluate a^3 - 27/a^3 when a^2 + 9/a^2 = 15. Advanced Factoring
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39
When A = x^3 + x -2 and B = x -2 find value of A^3 - B^3. Advanced Factoring
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40
Find value of a^2 b^2 + b^2 c^2 + c^2 a^2, when a^2 + b^2 + c^2 = 1, a+b+c =0, Advanced Factoring
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41
For a, b, c find value of a^3 + b^3 + c^3 when a^2 + b^2 + c^2 =12, 1/a + 1/b + 1/c = 3. Factoring
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42
For positive numbers a, b, a-b = 2, a^2 +ab + b^2, find the value of a^3 + b^3. Advanced Factoring
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43
When a^2 -3a +1 =0, evaluate 3a^2 + 4a^3 + a^4 + 3/a^2 + 4/a^3 + 1/a^4. Advanced Factoring
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44
When x - 1/x =3 evaluate x^2 + 1/x^2 and x^3 - 1/x^3. Advanced Factoring
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45
When x/2 = y/3 evaluate xy/(x^2 + y^2) and (2x^2 + 5xy)/(x^2 + y^2).
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46
When x^2 -3x -1 = 0 find value of x + 1/x, using advanced Factoring techniques
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47
Find value of expressions when a-b = 3, ab= -2 for a^3 -b^3, (a+b)^2, b/a + a/b. Advanced Factoring
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48
Find value of a^2 + b^2 when a + b = 2 and a^3 + b^3 =32. Advanced Factoring
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49
Use advanced factoring to factor 9x^2 +y^2 +4 -6xy-12x +4y, and -8x^3 + 12x^2 -6x +1
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50
Factor polynomial x^2(y-z) +y^2(z-x) + z^2(x-y). Advanced Factoring Techniques
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51
Factor polynomials by grouping x^3 - x^2y - xz^2 + yz^2 and x^2 y^2 -3xyz -xy + 3z.
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52
Factor each polynomial x^2 y^2 -3xy -xy +3z and x^4 -6x^2 +5. Advanced Factoring
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53
Factor polynomial (x-1)(x-2)(x+3)(x+4) -84. Advanced Factoring
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54
Factor polynomial x(x-1)(x^2 -x +1) -30. Advanced Factoring
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55
Factor polynomial x^2 +xy -4x -2y+4. Advanced Factoring
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56
Factor polynomial (x^2 -2x)^2 -2(x^2 -2x) -8. Advanced Factoring
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57
Factor polynomial x^4 + x^2 y^2 +y^4. Advanced Factoring
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58
Factor polynomial x^4 + 4x^2 +16. Advanced Factoring
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59
Factor polynomial x^4 +7x^2 + 16. Advanced Factoring
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60
For positive integer n, compute (-1)^(2n+1) times (-1)^(3n-1) times (-1)^(2n-1) divided by (-1)^(3n)
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61
Simplify 6^(x-y/x+y) when 10^x =2 and 10^y =3.
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62
Express 6^x using a and b when a = 2^(x+1) and b = 3^(x-1).
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63
Simplify expression (x+2)(x-2)(x-1)(x-5) using substitution and regrouping. Factoring
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64
Simplify expression (x^2 +x +3)(x^2 + x -1) using substitution. Polynomials
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65
Simplify expression (x+2y +1)(x-2y -1) using substitution. Polynomials
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66
Factor by Grouping y^2 -xy + x -y.
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67
Show that (a+b+c)(a+b-c) = (a + b)^2 - c^2. Special Factorization
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68
Prove that a^4 + b^4 = (a^2 + b^2)^2 -2a^2 b^2. Special Factorization.
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69
Prove that sin^4 x + cos^4 x = (sin^2 x+ cos^2 x)^2 - 2sin^2 x cos^2 x. Special Factorization
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70
Prove that a^3 + b^3 = (a+b)^3 - 3ab(a+b). Special Factorization
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71
Prove that sin^3 x + cos^3 x = (sin x + cos x)^3 - 3 sin x cos x ( sin x + cos x). Factorization
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72
Simplify sqrt(7 + 2 sqrt(10)) using a^2 + 2ab + b^2. Perfect Square Trinomial
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73
Simplify sqrt(3 + 2 sqrt(2)) using a^2 + 2ab + b^2. Perfect Square Trinomial
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74
Simplify sqrt(5 + 2 sqrt(6)) using a^2 + 2ab + b^2. Perfect Square Trinomial
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75
Simplify sqrt(7 + 2 sqrt(12)) using a^2 + 2ab + b^2. Perfect Square Trinomial
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76
Simplify sqrt(12 - 8sqrt(2)) using a^2 -2ab + b^2.
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77
Simplify sqrt(6 - 4sqrt(2)) using a^2 - 2ab + b^2.
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78
Simplify sqrt(3 - sqrt(2)) using a^2 -2ab + b^2
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79
How to factor x^4 +x^2 +1.
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80
Use quadratic techniques to solve n^6 - 1 =0. Factoring. Complex solutions
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81
Use quadratic techniques to solve y^(2/3) -7y^(1/3) + 12 = 0. Factoring
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82
Use quadratic techniques to solve y^(-2/3) - 7y^(-1/3) + 12 = 0. Factoring
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83
Use quadratic techniques to solve y^(-1) - 8y^(-1/2) + 12 = 0. Factoring
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84
Use quadratic techniques to solve y^3 - 28y^(3/2) + 27 = 0. Factoring
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85
Use quadratic techniques to solve t^(4/3) - 29t^(2/3) + 100 = 0. Factoring
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86
Use quadratic techniques to solve p^(2/3) - p^(1/3) - 20 = 0. Factoring
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87
Use quadratic techniques to solve x^(1/2) - 5x^(1/4) + 6 = 0. Factoring
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88
Use quadratic techniques to solve y^6 - 8y^3 = 0. Factoring
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89
Use quadratic techniques to solve n - sqrt(n) + 25 = 0. Factoring
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90
Use quadratic techniques to solve w - 12sqrt(w) + 27 = 0. Factoring
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91
Use quadratic techniques to solve n^4 - 49n^2 = 0. Factoring
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92
Use quadratic techniques to solve m^4 - 625 = 0. Factoring
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93
Use quadratic techniques to solve t^4 - 21t^2 + 80 = 0. Factoring
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94
Use quadratic techniques to solve x^4 -50x^2 + 49 = 0. Factoring
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95
Use quadratic techniques to solve x^4 - 29x^2 + 100 = 0. Factoring
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96
Use quadratic techniques to solve x- 5 sqrt(x) + 6 = 0. Factoring
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97
Use quadratic techniques to solve 1/x^2 - 7/x + 12 = 0. Factoring
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98
Use quadratic techniques to solve y^4 - 5y^2 +4 = 0. Factoring
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99
Use quadratic techniques to solve m^6 - 16m^3 + 64=0. Factoring
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100
Use quadratic techniques to solve x^4 - 6x^2 = -8. Factoring
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101
Use quadratic techniques to solve x^4 = 49. Factoring
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102
Write each equation in quadratic form. x^(1/8) + 2x^(1/16) + 1 = 0. X^8 + 2x^4 +1 =0
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103
Solve each equation by factoring 6e^3 = 5e^2 + 6e and 9 = 64p^2
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104
Solve each equation by factoring 6e^3 = 5e^2 + 6e and 9 = 64p^2
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105
Solve each equation by factoring 36k^2 = 25 and 12m^3 - 18m^2 = 15m
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106
Solve each equation by factoring 36k^2 = 25 and 12m^3 - 18m^2 = 15m
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107
Solve each equation by factoring 16v^2 +19v +6 =0 and 4j^2 +6 =11j
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108
Solve each equation by factoring 5w^2 -35w +60= 0 and 3d^2 + 24d +45 =0
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109
Solve each equation by factoring 7y^2 = 4y and c^2 = 2c +99
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110
Solve each equation by factoring n^2 + 25 = 10n and 9z = 10z^2
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111
Solve each equation by factoring x^2 - 4x -12 =0 and y^2 -16y +64 =0
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112
Solve equation by factoring-2x^2 -5x +12=0
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113
Solve equation by factoring 4k^2 - 35k -9 =0
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114
Solve each equation by factoring 3s^2 -13s =10 and 16x^2 = 49
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115
Solve each equation by factoring x^2 +3x -130=0 and x^2 -12x = -36
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116
Solve each equation by factoring x^2 + 13x +40 =0 and x^2 -7x -44=0
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117
Solve each equation by factoring z^2 x12z +27=0 and x^2 -4x -12= 0
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118
Factor completely 5y^5 + 135y^2. Sum of cubes. Factor 18p^3 - 51p^2 -135p. Trinomial
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119
Factor completely 81x^4 - 16. Difference of squares. Factor 4a^2 +12ab +9b^2 -25c^2
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120
Factor 45x^2 - 80y^2 and 36a^3b^2 + 66a^2b^3- 210ab^4
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121
Factor 4x^6 -4x^2 and k^3 -2k^2r -3kr^2
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122
Factor x^2 + 2x - xy -2y. Factor by grouping
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123
Factor by grouping 21-7t + 3r - rt
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124
Factor y^2 + 20 y + 96 and 6a^2 + 11a -2. Trinomials
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125
Factor 4a^2 + a - 3 and 2t^3 + 32t^2 - 128t
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126
Factor trinomials x^2 -3x -10 and r^3 -3r^2 - 54r. Greatest common factor
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127
Factor 8m^3 -1 and b^4 - 81. Difference of Squares and difference of cubes
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128
Factor 2y^2 - 242 and x^3 +8. Difference of Squares. Sum of Cubes. Greatest common factor
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129
Factor 16x^2 - 169 and c^2 -49. Difference of Squares
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130
Factor 15a^2b - 10ab^2.
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131
Factor c^4 + c^3 - c^2 -c by grouping. Factor x^6 -1 by sum and difference of cubes.
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132
Factor c^4 + c^3 - c^2 -c by grouping. Factor x^6 -1 by sum and difference of cubes.
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133
Factor by highest or greatest common factor. 2m^5 - 12m^3 +18. Perfect square trinomial
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134
Factor 4m^6 - 12m^3 +9 and x^3 - 343. Perfect Square Trinomials and difference of perfect cubes
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135
Factor 162x^6 - 98 and also a perfect square trinomial
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136
Factor 2r^3 +250 and 100m^8 -9. Special Factorisation
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137
Factor completely x^4 -1 and 35x^3y^4 - 60x^4y
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138
How to factor by grouping xm + xn + ym + yn
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139
How to factor 125c^6+1 and m^12n^3 -27. Difference and sum of cubes.
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140
How to factor 2m^2 - 98. Difference of perfect squares
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141
How to factor with difference of squares with radicals square
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142
How to factorize with complex numbers and radicals
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143
Which expression is equivalent to quadratic expression by factoring 24x^2 - 22x + 5
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144
Find an equivalent equation by factoring y = 3(x +2)^2 +7
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145
Find an equivalent function by factoring 9x^2 -24x +16
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146
Find a positive solution by factoring quadratic equation 4x^2 + 12x =135
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147
Write an equivalent expression by factoring with greatest common factor 210d^2 -63d
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148
Find an equivalent function by factoring trinomial
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149
Find the factors of x^3 - 64 with difference of cubes
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150
Write rational expression in simplest from. Difference of squares. Factoring trinomials
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151
Simplify rational expression with factor by grouping and difference of squares
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152
Simplify expression using factoring facts of trinomials
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153
Over the set of integers factor a quartic expression
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154
Find real and complex roots by factoring by grouping
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155
Find an equivalent expression by grouping and difference of squares
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156
Find the values of x by simplifying and factoring
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157
How To Factor And Solve a Cubic Equation. Correction from previous video
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158
Special Factorization. Part 6
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159
Special Factorization. Part 5
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160
Special Factorization. Part 4
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161
Special Factorization. Part 3
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162
Special Factorization. Part 2
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163
Special Factorization. Part 1
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164
Factor the following expressions
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165
Factor Each Polynomial Expressions. Examples
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166
Factor the following expressions
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167
Reduce each Rational Expression Into Lowest Terms
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168
How To Factor And Solve Polynomials
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169
How To Factor a Quartic Function
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170
How to factor. Sum and Difference of Cubes
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171
How to factor trinomials with different degrees
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172
How to factor trinomials with degree of eight GCF or HCF
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173
How to factor trinomials with degree of six
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174
How to factor by grouping and the GCF (HCF)
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175
How To Factor by grouping and sum and difference of cubes
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176
How To Factor by Grouping
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177
How To Factor, review sum and difference of cubes and more
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