7.1 Greatest Common Factor and Factor by Grouping

Before you get started, take this readiness quiz.

Factor 56 into primes.
If you missed this problem, review the reference.

Find the least common multiple of 18 and 24.
If you missed this problem, review the reference.

Simplify $−3 \left(6 a + 11\right)$.
If you missed this problem, review the reference.

Find the GCF of 48 and 80.

Find the GCF of 18 and 40.

Find the GCF: $12 x^{2} , 18 x^{3}$.

Find the GCF: $16 y^{2} , 24 y^{3}$.

Find the GCF: $6 a b^{4} , 8 a^{2} b$.

Find the GCF: $9 m^{5} n^{2} , 12 m^{3} n$.

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

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

Factor: $6 a + 24$.

Factor: $2 b + 14$.

Factor: $14 x + 14$.

Factor: $12 p + 12$.

Factor: $18 u - 36$.

Factor: $30 y - 60$.

Factor: $5 x^{2} - 25 x + 15$.

Factor: $3 y^{2} - 12 y + 27$.

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

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

Factor: $20 x^{3} - 10 x^{2} + 14 x$.

Factor: $24 y^{3} - 12 y^{2} - 20 y$.

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

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

Factor: $−16 z - 64$.

Factor: $−9 y - 27$.

Factor: $−4 b^{2} + 16 b$.

Factor: $−7 a^{2} + 21 a$.

Factor: $4 m \left(m + 3\right) - 7 \left(m + 3\right)$.

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

Factor: $x y + 8 y + 3 x + 24$.

Factor: $a b + 7 b + 8 a + 56$.

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

Factor: $x^{2} + 2 x - 5 x - 10$.

Factor: $y^{2} + 4 y - 7 y - 28$.

Find the greatest common factor.

8, 18

Find the greatest common factor.

72, 162

Find the greatest common factor.

10a, 50

Find the greatest common factor.

$3 x , 10 x^{2}$

Find the greatest common factor.

$8 w^{2} , 24 w^{3}$

Find the greatest common factor.

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

Find the greatest common factor.

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

Find the greatest common factor.

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

Find the greatest common factor.

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

Factor the greatest common factor from each polynomial.

$4 x + 20$

Factor the greatest common factor from each polynomial.

$6 m + 9$

Factor the greatest common factor from each polynomial.

$9 q + 9$

Factor the greatest common factor from each polynomial.

$8 m - 8$

Factor the greatest common factor from each polynomial.

$9 n - 63$

Factor the greatest common factor from each polynomial.

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

Factor the greatest common factor from each polynomial.

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

Factor the greatest common factor from each polynomial.

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

Factor the greatest common factor from each polynomial.

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

Factor the greatest common factor from each polynomial.

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

Factor the greatest common factor from each polynomial.

$−2 x - 4$

Factor the greatest common factor from each polynomial.

$5 x \left(x + 1\right) + 3 \left(x + 1\right)$

Factor the greatest common factor from each polynomial.

$3 b \left(b - 2\right) - 13 \left(b - 2\right)$

Factor by grouping.

$x y + 2 y + 3 x + 6$

Factor by grouping.

$u v - 9 u + 2 v - 18$

Factor by grouping.

$b^{2} + 5 b - 4 b - 20$

Factor by grouping.

$p^{2} + 4 p - 9 p - 36$

Factor.

$−20 x - 10$

Factor.

$3 x^{3} - 7 x^{2} + 6 x - 14$

Factor.

$x^{2} + x y + 5 x + 5 y$

Area of a rectangle The area of a rectangle with length 6 less than the width is given by the expression $w^{2} - 6 w$, where $w =$ width. Factor the greatest common factor from the polynomial.

The greatest common factor of 36 and 60 is 12. Explain what this means.