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6.2 Factor Trinomials

Finding two numbers that hit a target sum and product, trial and error versus the ac method once the leading coefficient exceeds one, and substitution.

Intermediate Algebra 2e, 6.2 Factor Trinomials

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85 exercises

6.2 Exercise 1

Before you get started, take this readiness quiz.

Find all the factors of 72.
If you missed this problem, review the reference.

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6.2 Exercise 2

Find the product: (3y+4)(2y+5).\left(3 y + 4\right) \left(2 y + 5\right) .
If you missed this problem, review the reference.

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6.2 Exercise 3

Simplify: −9(6);−9 \left(6\right) ; −9(−6).−9 \left(−6\right) .
If you missed this problem, review the reference.

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6.2 Exercise 5

Factor: q2+10q+24.q^{2} + 10 q + 24 .

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6.2 Exercise 6

Factor: t2+14t+24.t^{2} + 14 t + 24 .

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6.2 Exercise 7

Factor: y2−11y+28.y^{2} - 11 y + 28.

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6.2 Exercise 8

Factor: u2−9u+18.u^{2} - 9 u + 18 .

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6.2 Exercise 9

Factor: y2−16y+63.y^{2} - 16 y + 63 .

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6.2 Exercise 10

Factor: 2x+x2−48.2 x + x^{2} - 48 .

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6.2 Exercise 11

Factor: 9m+m2+18.9 m + m^{2} + 18 .

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6.2 Exercise 12

Factor: −7n+12+n2.−7 n + 12 + n^{2} .

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6.2 Exercise 13

Factor: r2−8rs−9s2.r^{2} - 8 r s - 9 s^{2} .

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6.2 Exercise 14

Factor: a2−11ab+10b2.a^{2} - 11 a b + 10 b^{2} .

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6.2 Exercise 15

Factor: m2−13mn+12n2.m^{2} - 13 m n + 12 n^{2} .

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6.2 Exercise 16

Factor: u2−9uv−12v2.u^{2} - 9 u v - 12 v^{2} .

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6.2 Exercise 17

Factor: x2−7xy−10y2.x^{2} - 7 x y - 10 y^{2} .

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6.2 Exercise 18

Factor: p2+15pq+20q2.p^{2} + 15 p q + 20 q^{2} .

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6.2 Exercise 19

Factor completely: 4x3+16x2−20x.4 x^{3} + 16 x^{2} - 20 x .

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6.2 Exercise 20

Factor completely: 5x3+15x2−20x.5 x^{3} + 15 x^{2} - 20 x .

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6.2 Exercise 21

Factor completely: 6y3+18y2−60y.6 y^{3} + 18 y^{2} - 60 y .

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6.2 Exercise 23

Factor completely using trial and error: 2a2+5a+3.2 a^{2} + 5 a + 3 .

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6.2 Exercise 24

Factor completely using trial and error: 4b2+5b+1.4 b^{2} + 5 b + 1 .

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6.2 Exercise 26

Factor completely using trial and error: 8x2−14x+3.8 x^{2} - 14 x + 3 .

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6.2 Exercise 27

Factor completely using trial and error: 10y2−37y+7.10 y^{2} - 37 y + 7 .

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6.2 Exercise 29

Factor completely using trial and error 18x2−3xy−10y2.18 x^{2} - 3 x y - 10 y^{2} .

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6.2 Exercise 30

Factor completely using trial and error: 30x2−53xy−21y2.30 x^{2} - 53 x y - 21 y^{2} .

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6.2 Exercise 32

Factor completely using trial and error: 15n3−85n2+100n.15 n^{3} - 85 n^{2} + 100 n .

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6.2 Exercise 33

Factor completely using trial and error: 56q3+320q2−96q.56 q^{3} + 320 q^{2} - 96 q .

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6.2 Exercise 35

Factor using the ‘ac’ method: 6x2+13x+2.6 x^{2} + 13 x + 2 .

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6.2 Exercise 36

Factor using the ‘ac’ method: 4y2+8y+3.4 y^{2} + 8 y + 3 .

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6.2 Exercise 38

Factor using the ‘ac’ method: 16x2−32x+12.16 x^{2} - 32 x + 12 .

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6.2 Exercise 39

Factor using the ‘ac’ method: 18w2−39w+18.18 w^{2} - 39 w + 18 .

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6.2 Exercise 41

Factor by substitution: h4+4h2−12.h^{4} + 4 h^{2} - 12 .

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6.2 Exercise 42

Factor by substitution: y4−y2−20.y^{4} - y^{2} - 20 .

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6.2 Exercise 44

Factor by substitution: (x−5)2+6(x−5)+8.\left(x - 5\right)^{2} + 6 \left(x - 5\right) + 8 .

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6.2 Exercise 45

Factor by substitution: (y−4)2+8(y−4)+15.\left(y - 4\right)^{2} + 8 \left(y - 4\right) + 15 .

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6.2 Exercise 46

Factor each trinomial of the form x2+bx+c.x^{2} + b x + c .

p2+11p+30p^{2} + 11 p + 30

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6.2 Exercise 48

Factor each trinomial of the form x2+bx+c.x^{2} + b x + c .

n2+19n+48n^{2} + 19 n + 48

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6.2 Exercise 50

Factor each trinomial of the form x2+bx+c.x^{2} + b x + c .

a2+25a+100a^{2} + 25 a + 100

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6.2 Exercise 52

Factor each trinomial of the form x2+bx+c.x^{2} + b x + c .

x2−8x+12x^{2} - 8 x + 12

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6.2 Exercise 54

Factor each trinomial of the form x2+bx+c.x^{2} + b x + c .

y2−18y+45y^{2} - 18 y + 45

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6.2 Exercise 56

Factor each trinomial of the form x2+bx+c.x^{2} + b x + c .

x2−8x+7x^{2} - 8 x + 7

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6.2 Exercise 58

Factor each trinomial of the form x2+bx+c.x^{2} + b x + c .

5p−6+p25 p - 6 + p^{2}

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6.2 Exercise 60

Factor each trinomial of the form x2+bx+c.x^{2} + b x + c .

8−6x+x28 - 6 x + x^{2}

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6.2 Exercise 62

Factor each trinomial of the form x2+bx+c.x^{2} + b x + c .

x2−12−11xx^{2} - 12 - 11 x

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6.2 Exercise 64

Factor each trinomial of the form x2+bxy+cy2.x^{2} + b x y + c y^{2} . If the trinomial cannot be factored, answer “Prime.”

x2−2xy−80y2x^{2} - 2 x y - 80 y^{2}

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6.2 Exercise 66

Factor each trinomial of the form x2+bxy+cy2.x^{2} + b x y + c y^{2} . If the trinomial cannot be factored, answer “Prime.”

m2−64mn−65n2m^{2} - 64 m n - 65 n^{2}

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6.2 Exercise 68

Factor each trinomial of the form x2+bxy+cy2.x^{2} + b x y + c y^{2} . If the trinomial cannot be factored, answer “Prime.”

a2+5ab−24b2a^{2} + 5 a b - 24 b^{2}

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6.2 Exercise 70

Factor each trinomial of the form x2+bxy+cy2.x^{2} + b x y + c y^{2} . If the trinomial cannot be factored, answer “Prime.”

x2−3xy−14y2x^{2} - 3 x y - 14 y^{2}

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6.2 Exercise 72

Factor each trinomial of the form x2+bxy+cy2.x^{2} + b x y + c y^{2} . If the trinomial cannot be factored, answer “Prime.”

m2−5mn+30n2m^{2} - 5 m n + 30 n^{2}

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6.2 Exercise 74

Factor completely using trial and error.

p3−8p2−20pp^{3} - 8 p^{2} - 20 p

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6.2 Exercise 76

Factor completely using trial and error.

3m3−21m2+30m3 m^{3} - 21 m^{2} + 30 m

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6.2 Exercise 78

Factor completely using trial and error.

5x4+10x3−75x25 x^{4} + 10 x^{3} - 75 x^{2}

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6.2 Exercise 80

Factor completely using trial and error.

2t2+7t+52 t^{2} + 7 t + 5

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6.2 Exercise 82

Factor completely using trial and error.

11x2+34x+311 x^{2} + 34 x + 3

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6.2 Exercise 84

Factor completely using trial and error.

4w2−5w+14 w^{2} - 5 w + 1

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6.2 Exercise 86

Factor completely using trial and error.

4q2−7q−24 q^{2} - 7 q - 2

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6.2 Exercise 88

Factor completely using trial and error.

6p2−19pq+10q26 p^{2} - 19 p q + 10 q^{2}

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6.2 Exercise 90

Factor completely using trial and error.

4a2+17ab−15b24 a^{2} + 17 a b - 15 b^{2}

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6.2 Exercise 92

Factor completely using trial and error.

−16x2−32x−16−16 x^{2} - 32 x - 16

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6.2 Exercise 94

Factor completely using trial and error.

−30q3−140q2−80q−30 q^{3} - 140 q^{2} - 80 q

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6.2 Exercise 96

Factor using the ‘ac’ method.

5n2+21n+45 n^{2} + 21 n + 4

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6.2 Exercise 98

Factor using the ‘ac’ method.

4k2−16k+154 k^{2} - 16 k + 15

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6.2 Exercise 100

Factor using the ‘ac’ method.

6y2+y−156 y^{2} + y - 15

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6.2 Exercise 102

Factor using the ‘ac’ method.

2n2−27n−452 n^{2} - 27 n - 45

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6.2 Exercise 104

Factor using the ‘ac’ method.

60y2+290y−5060 y^{2} + 290 y - 50

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6.2 Exercise 106

Factor using the ‘ac’ method.

48z3−102z2−45z48 z^{3} - 102 z^{2} - 45 z

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6.2 Exercise 108

Factor using the ‘ac’ method.

16s2+40s+2416 s^{2} + 40 s + 24

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6.2 Exercise 110

Factor using the ‘ac’ method.

48y2+12y−3648 y^{2} + 12 y - 36

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6.2 Exercise 112

Factor using substitution.

x4−6x2−7x^{4} - 6 x^{2} - 7

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6.2 Exercise 114

Factor using substitution.

x4−3x2−28x^{4} - 3 x^{2} - 28

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6.2 Exercise 116

Factor using substitution.

(x−3)2−5(x−3)−36\left(x - 3\right)^{2} - 5 \left(x - 3\right) - 36

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6.2 Exercise 118

Factor using substitution.

(3y−2)2−(3y−2)−2\left(3 y - 2\right)^{2} - \left(3 y - 2\right) - 2

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6.2 Exercise 120

Factor each expression using any method.

u2−12u+36u^{2} - 12 u + 36

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6.2 Exercise 122

Factor each expression using any method.

r2−20rs+64s2r^{2} - 20 r s + 64 s^{2}

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6.2 Exercise 124

Factor each expression using any method.

12y2−29y+1412 y^{2} - 29 y + 14

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6.2 Exercise 126

Factor each expression using any method.

6n2+5n−46 n^{2} + 5 n - 4

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6.2 Exercise 128

Factor each expression using any method.

13z2+39z−2613 z^{2} + 39 z - 26

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6.2 Exercise 130

Factor each expression using any method.

3p2+21p3 p^{2} + 21 p

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6.2 Exercise 132

Factor each expression using any method.

6r2+30r+366 r^{2} + 30 r + 36

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6.2 Exercise 134

Factor each expression using any method.

24n2+20n+424 n^{2} + 20 n + 4

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6.2 Exercise 136

Factor each expression using any method.

x4−4x2−12x^{4} - 4 x^{2} - 12

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6.2 Exercise 138

Factor each expression using any method.

(x+3)2−9(x+3)−36\left(x + 3\right)^{2} - 9 \left(x + 3\right) - 36

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6.2 Exercise 140

Many trinomials of the form x2+bx+cx^{2} + b x + c factor into the product of two binomials (x+m)(x+n).\left(x + m\right) \left(x + n\right) . Explain how you find the values of m and n.

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6.2 Exercise 142

List, in order, all the steps you take when using the “ac” method to factor a trinomial of the form ax2+bx+c.a x^{2} + b x + c .

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Adapted from Intermediate Algebra 2e © 2020 Rice University. Licensed under CC BY 4.0. Source: Intermediate Algebra 2e. Imported at revision 77a933c.