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Factoring

Intermediate Algebra · 540 exercises

Q. 6.92

Solve, $36 x^{2} = 121$

4 step solution

Q. 272

In the following exercises, factor completely $(4 x - 5)^{2} - 7 (4 x - 5) + 12$

3 step solution

Q. 273

Explain what it mean to factor a polynomial completely.

2 step solution

Q. 6.1

Find the greatest common factors: $25 m^{4}, 35 m^{3}, 20 m^{2}$ .

2 step solution

Q. 6.2

Find the greatest common factors: $14 x^{3}, 70 x^{2}, 105 x$ .

2 step solution

Q. 6.3

Factor: $9 x y^{2} + 6 x^{2} y^{2} + 21 y^{3}$ .

4 step solution

Q. 6.4

Factor: $3 p^{3} - 6 p^{2} q + 9 p q^{3}$

4 step solution

Q. 6.5

Factor: $2 x^{3} + 12 x^{2}$

4 step solution

Q. 6.6

Factor: $6 y^{3} - 15 y^{2}$

4 step solution

Q. 6.7

Factor: $15 x^{3} y - 3 x^{2} y^{2} + 6 x y^{3}$

4 step solution

Q. 6.8

Factor: $8 a^{3} b + 2 a^{2} b^{2} - 6 a b^{3}$ .

4 step solution

Q. 6.9

Factor: $- 4 b^{3} + 16 b^{2} - 8 b$

3 step solution

Q. 6.10

Factor: $- 7 a^{3} + 21 a^{2} - 14 a$

3 step solution

Q. 6.12

Factor: $8 n (n - 4) + 5 (n - 4)$ .

3 step solution

Q. 6.13

Factor by grouping: $x y + 8 y + 3 x + 24$

3 step solution

Q. 6.14

Factor by grouping: $a b + 7 b + 8 a + 56$

3 step solution

Q. 6.15

Factor by grouping:

a) $x^{2} + 2 x - 5 x - 10$

b) $20 x^{2} - 16 x - 15 x + 12$

4 step solution

Q. 6.16

Factor by grouping:

a) $y^{2} + 4 y - 7 y - 28$

b) $42 m^{2} - 18 m - 35 m + 15$

4 step solution

Q. 1

In the following exercises, find the greatest common factor.

$10 p^{3} q, 12 p q^{2}$

2 step solution

Q. 2

In the following exercises, find the greatest common factor.

$8 a^{2} b^{3}, 10 a b^{2}$

2 step solution

Q. 3

In the following exercises, find the greatest common factor.

$12 m^{2} n^{3}, 30 m^{5} n^{3}$

2 step solution

Q. 4

In the following exercises, find the greatest common factor.

$28 x^{2} y^{4}, 42 x^{4} y^{4}$

2 step solution

Q. 5

In the following exercises, find the greatest common factor.

$10 a^{3}, 12 a^{2}, 14 a$

2 step solution

Q. 6

In the following exercises, find the greatest common factor.

$20 y^{3}, 28 y^{2}, 40 y$

2 step solution

Q. 7

In the following exercises, find the greatest common factor.

$35 x^{3} y^{2}, 10 x^{4} y, 5 x^{5} y^{3}$

2 step solution

Q. 8

In the following exercises, find the greatest common factor.

$27 p^{2} q^{3}, 45 p^{3} q^{4}, 9 p^{4} q^{3}$

2 step solution

Q. 9

In the following exercises, factor the greatest common factor from each polynomial.

$6 m + 9$

4 step solution

Q. 10

In the following exercises, factor the greatest common factor from each polynomial.

$14 p + 35$

4 step solution

Q. 12

In the following exercises, factor the greatest common factor from each polynomial.

$45 b - 18$

4 step solution

Q. 13

In the following exercises, factor the greatest common factor from each polynomial.

$3 x^{2} + 6 x - 9$

4 step solution

Q. 14

In the following exercises, factor the greatest common factor from each polynomial.

$14 p + 35$

4 step solution

Q. 15

In the following exercises, factor the greatest common factor from each polynomial.

$8 p^{2} + 4 p + 2$

4 step solution

Q. 16

In the following exercises, factor the greatest common factor from each polynomial.

$10 q^{2} + 14 q + 20$

4 step solution

Q. 17

In the following exercises, factor the greatest common factor from each polynomial.

$8 y^{3} + 16 y^{2}$

4 step solution

Q. 18

In the following exercises, factor the greatest common factor from each polynomial.

$12 x^{3} - 10 x$

4 step solution

Q. 19

In the following exercises, factor the greatest common factor from each polynomial.

$5 x^{3} - 15 x^{2} + 20 x$

4 step solution

Q. 20

In the following exercises, factor the greatest common factor from each polynomial.

$8 m^{2} - 40 m + 16$

4 step solution

Q. 21

In the following exercises, factor the greatest common factor from each polynomial.

$24 x^{3} - 12 x^{2} + 15 x$

4 step solution

Q. 22

In the following exercises, factor the greatest common factor from each polynomial.

$24 y^{3} - 18 y^{2} - 30 y$

4 step solution

Q 23E

In the following exercises, factor the greatest common factor from each polynomial.

$12 x y^{2} + 18 x^{2} y^{2} - 30 y^{3}$

5 step solution

Q 25

In the following exercises, factor the greatest common factor from each polynomial.

$24 y^{3} - 18 y^{2} - 30 y$

5 step solution

Q 26E

In the following exercises, factor the greatest common factor from each polynomial.

$24 a^{3} b + 6 a^{2} b^{2} - 18 a b^{3}$

5 step solution

Q 27E

In the following exercises, factor the greatest common factor from each polynomial.

$- 2 x - 4$

5 step solution

Q 28E

In the following exercises, factor the greatest common factor from each polynomial.

$- 3 b + 12$

5 step solution

Q 29E

In the following exercises, factor the greatest common factor from each polynomial.

$- 2 x^{3} + 18 x^{2} - 8 x$

5 step solution

Q 30E

In the following exercises, factor the greatest common factor from each polynomial.

$- 5 y^{3} + 35 y^{2} - 15 y$

5 step solution

Q 31E

In the following exercises, factor the greatest common factor from each polynomial.

- 4 p^{3} q - 12 p^{2} q^{2} + 16 p q^{2}

5 step solution

Q 33

In the following exercises, factor the greatest common factor from each polynomial.

$5 x (x + 1) + 3 (x + 1)$

3 step solution

Q 34

In the following exercises, factor the greatest common factor from each polynomial.

$2 x (x - 1) + 9 (x - 1)$

3 step solution

Q 35

In the following exercises, factor the greatest common factor from each polynomial.

$3 b (b - 2) - 13 (b - 2)$

3 step solution

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