7.5 General Strategy for Factoring Polynomials

A decision order for any polynomial: common factor first, then count the terms to pick the pattern or method, and keep going until nothing splits further.

Elementary Algebra 2e, 7.5 General Strategy for Factoring Polynomials

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49 exercises

7.5 Exercise 1

Before you get started, take this readiness quiz.

Factor $y^{2} - 2 y - 24$ .
If you missed this problem, review the reference.

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7.5 Exercise 2

Factor $3 t^{2} + 17 t + 10$ .
If you missed this problem, review the reference.

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7.5 Exercise 3

Factor $36 p^{2} - 60 p + 25$ .
If you missed this problem, review the reference.

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7.5 Exercise 4

Factor $5 x^{2} - 80$ .
If you missed this problem, review the reference.

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7.5 Exercise 5

Factor completely: $4 x^{5} + 12 x^{4}$ .

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7.5 Exercise 6

Factor completely: $3 a^{4} + 18 a^{3}$ .

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7.5 Exercise 7

Factor completely: $45 b^{6} + 27 b^{5}$ .

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7.5 Exercise 9

Factor completely: $10 a^{2} - 17 a + 6$ .

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7.5 Exercise 10

Factor completely: $8 x^{2} - 18 x + 9$ .

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7.5 Exercise 11

Factor completely: $g^{3} + 25 g$ .

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7.5 Exercise 12

Factor completely: $x^{3} + 36 x$ .

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7.5 Exercise 13

Factor completely: $27 y^{2} + 48$ .

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7.5 Exercise 14

Factor completely: $12 y^{2} - 75$ .

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7.5 Exercise 15

Factor completely: $16 x^{3} - 36 x$ .

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7.5 Exercise 16

Factor completely: $27 y^{2} - 48$ .

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7.5 Exercise 18

Factor completely: $4 x^{2} + 20 x y + 25 y^{2}$ .

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7.5 Exercise 19

Factor completely: $9 m^{2} + 42 m n + 49 n^{2}$ .

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7.5 Exercise 20

Factor completely: $6 y^{2} - 18 y - 60$ .

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7.5 Exercise 21

Factor completely: $8 y^{2} + 16 y - 24$ .

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7.5 Exercise 22

Factor completely: $5 u^{2} - 15 u - 270$ .

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7.5 Exercise 24

Factor completely: $250 m^{3} + 432$ .

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7.5 Exercise 25

Factor completely: $81 q^{3} + 192$ .

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7.5 Exercise 26

Factor completely: $2 x^{4} - 32$ .

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7.5 Exercise 27

Factor completely: $4 a^{4} - 64$ .

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7.5 Exercise 28

Factor completely: $7 y^{4} - 7$ .

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7.5 Exercise 29

Factor completely: $3 x^{2} + 6 b x - 3 a x - 6 a b$ .

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7.5 Exercise 30

Factor completely: $6 x^{2} - 12 x c + 6 b x - 12 b c$ .

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7.5 Exercise 31

Factor completely: $16 x^{2} + 24 x y - 4 x - 6 y$ .

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7.5 Exercise 32

Factor completely: $10 x^{2} - 34 x - 24$ .

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7.5 Exercise 33

Factor completely: $4 p^{2} - 16 p + 12$ .

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7.5 Exercise 34

Factor completely: $6 q^{2} - 9 q - 6$ .

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7.5 Exercise 35

Factor completely.

$10 x^{4} + 35 x^{3}$

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7.5 Exercise 37

Factor completely.

$y^{2} + 10 y - 39$

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7.5 Exercise 39

Factor completely.

$2 n^{2} + 13 n - 7$

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7.5 Exercise 41

Factor completely.

$a^{5} + 9 a^{3}$

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7.5 Exercise 43

Factor completely.

$121 r^{2} - s^{2}$

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7.5 Exercise 45

Factor completely.

$8 m^{2} - 32$

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7.5 Exercise 47

Factor completely.

$25 w^{2} - 60 w + 36$

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7.5 Exercise 49

Factor completely.

$m^{2} + 14 m n + 49 n^{2}$

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7.5 Exercise 51

Factor completely.

$7 b^{2} + 7 b - 42$

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7.5 Exercise 53

Factor completely.

$3 x^{3} - 81$

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7.5 Exercise 55

Factor completely.

$k^{4} - 16$

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7.5 Exercise 57

Factor completely.

$15 p q - 15 p + 12 q - 12$

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7.5 Exercise 59

Factor completely.

$4 x^{2} + 40 x + 84$

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7.5 Exercise 61

Factor completely.

$u^{5} + u^{2}$

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7.5 Exercise 63

Factor completely.

$4 c^{2} + 20 c d + 81 d^{2}$

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7.5 Exercise 65

Factor completely.

$10 m^{4} - 6250$

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7.5 Exercise 67

Watermelon drop A springtime tradition at the University of California San Diego is the Watermelon Drop, where a watermelon is dropped from the seventh story of Urey Hall.

ⓐ The binomial $−16 t^{2} + 80$ gives the height of the watermelon $t$ seconds after it is dropped. Factor the greatest common factor from this binomial.
ⓑ If the watermelon is thrown down with initial velocity 8 feet per second, its height aft…

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7.5 Exercise 69

The difference of squares $y^{4} - 625$ can be factored as $\left(y^{2} - 25\right) \left(y^{2} + 25\right)$ . But it is not completely factored. What more must be done to completely factor it?

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