6.1 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 (LCM) of 18 and 24.
If you missed this problem, review the reference.

Multiply: $−3 a \left(7 a + 8 b\right) .$
If you missed this problem, review the reference.

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

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

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

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

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

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

Factor: $−4 b^{3} + 16 b^{2} - 8 b .$

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

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

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

Factor by grouping: ⓐ $x^{2} + 3 x - 2 x - 6$ ⓑ $6 x^{2} - 3 x - 4 x + 2 .$

Factor by grouping: ⓐ $x^{2} + 2 x - 5 x - 10$ ⓑ $20 x^{2} - 16 x - 15 x + 12 .$

Factor by grouping: ⓐ $y^{2} + 4 y - 7 y - 28$ ⓑ $42 m^{2} - 18 m - 35 m + 15 .$

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.

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

Factor the greatest common factor from each polynomial.

$6 m + 9$

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.

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

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.

$20 x^{3} y - 4 x^{2} y^{2} + 12 x y^{3}$

Factor the greatest common factor from each polynomial.

$−2 x - 4$

Factor the greatest common factor from each polynomial.

$−2 x^{3} + 18 x^{2} - 8 x$

Factor the greatest common factor from each polynomial.

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

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.

$a b + 5 a + 3 b + 15$

Factor by grouping.

$8 y^{2} + y + 40 y + 5$

Factor by grouping.

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

Factor by grouping.

$u^{2} - u + 6 u - 6$

Factor by grouping.

$9 p^{2} + 12 p - 15 p - 20$

Factor by grouping.

$m n - 6 m - 4 n + 24$

Factor by grouping.

$2 x^{2} - 14 x - 5 x + 35$

Factor.

$−18 x y^{2} - 27 x^{2} y$

Factor.

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

Factor.

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

What does it mean to say a polynomial is in factored form?

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