Chapter 6

Factor the following problems, if possible. $$ 10 x^{2}+33 x+20 $$

For the following problems, use the grouping method to factor the polynomials. Some polynomials may not. be factorable using the grouping method. $$ 4 p q-7 p+3 q^{2}-21 $$

In the following problems, the first quantity represents the product and the second quantity represents a factor of that product. Find the other factor. $$ 147 a^{20} b^{6} c^{18} d^{2}, \quad 21 a^{3} b d $$

For the following problems, factor the polynomials. $$ a x^{2}-a $$

For the following problems, factor the binomials. $$ 2 b^{2}-32 $$

For the following problems, factor the trinomials when possible. $$ x^{2}+6 x-16 $$

Factor the following problems, if possible. $$ 3 x^{2}-x-4 $$

For the following problems, use the grouping method to factor the polynomials. Some polynomials may not. be factorable using the grouping method. $$ 8 x^{2}+16 x y-5 x-10 y $$

For the following problems, the first quantity represents the product and the second quantity a factor. Find the other factor. $$ 21 x^{2}+7 x-14,7 $$

In the following problems, the first quantity represents the product and the second quantity represents a factor of that product. Find the other factor. $$ -121 a^{6} b^{8} c^{10}, 11 b^{2} c^{5} $$

For the following problems, factor the polynomials. $$ b y^{2}+b $$

For the following problems, factor the binomials. $$ 3 x^{2}-27 $$

For the following problems, factor the trinomials when possible. $$ y^{2}-8 y+7 $$

Factor the following problems, if possible. $$ 3 x^{2}+x-4 $$

For the following problems, use the grouping method to factor the polynomials. Some polynomials may not. be factorable using the grouping method. $$ 12 s^{2}-27 s-8 s t+18 t $$

In the following problems, the first quantity represents the product and the second quantity represents a factor of that product. Find the other factor. $$ \frac{1}{8} x^{4} y^{3}, \quad \frac{1}{2} x y^{3} $$

For the following problems, factor the polynomials. $$ 7 b y^{2}+14 b $$

For the following problems, factor the binomials. $$ 5 x^{2}-125 $$

For the following problems, factor the trinomials when possible. $$ y^{2}-5 y-24 $$

Factor the following problems, if possible. $$ 4 x^{2}+8 x-21 $$

For the following problems, use the grouping method to factor the polynomials. Some polynomials may not. be factorable using the grouping method. $$ 15 x^{2}-12 x-10 x y+8 y $$

For the following problems, the first quantity represents the product and the second quantity a factor. Find the other factor. $$ 14 y^{2}-28 y+14, \quad 14 $$

In the following problems, the first quantity represents the product and the second quantity represents a factor of that product. Find the other factor. $$ 7 x^{2} y^{3} z^{2}, \quad 7 x^{2} y^{3} z $$

For the following problems, factor the binomials. $$ 4 a^{2}-25 $$

For the following problems, factor the trinomials when possible. $$ a^{2}+a-30 $$

Factor the following problems, if possible. $$ 2 a^{2}-a-3 $$

For the following problems, use the grouping method to factor the polynomials. Some polynomials may not. be factorable using the grouping method. $$ a^{4} b^{4}+3 a^{5} b^{5}+2 a^{2} b^{2}+6 a^{3} b^{3} $$

For the following problems, factor the polynomials. $$ 5 a^{2} x^{2}+10 x $$

In the following problems, the first quantity represents the product and the second quantity represents a factor of that product. Find the other factor. $$ 5 a^{4} b^{7} c^{3} d^{2}, 5 a^{4} b^{7} c^{3} d $$

For the following problems, factor the polynomials. $$ 24 a x^{2}+28 a $$

For the following problems, factor the binomials. $$ 9 x^{2}-100 $$

For the following problems, factor the trinomials when possible. $$ a^{2}-3 a+2 $$

Factor the following problems, if possible. $$ 9 a^{2}-7 a+2 $$

For the following problems, use the grouping method to factor the polynomials. Some polynomials may not. be factorable using the grouping method. $$ 4 a^{3} b c-14 a^{2} b c^{3}+10 a b c^{2}-35 b c^{4} $$

For the following problems, the first quantity represents the product and the second quantity a factor. Find the other factor. $$ 4 y^{2}-10 y-12, \quad 2 $$

In the following problems, the first quantity represents the product and the second quantity represents a factor of that product. Find the other factor. $$ 14 x^{4} y^{3} z^{7}, 14 x^{4} y^{3} z^{7} $$

For the following problems, factor the polynomials. $$ 10 x^{2}+5 x-15 $$

For the following problems, factor the binomials. $$ 36 y^{2}-25 $$

For the following problems, factor the trinomials when possible. $$ a^{2}-12 a+20 $$

For the following problems, use the grouping method to factor the polynomials. Some polynomials may not. be factorable using the grouping method. $$ 5 x^{2} y^{3} z+3 x^{3} y w-10 y^{3} z^{2}-6 w x y z $$

For the following problems, the first quantity represents the product and the second quantity a factor. Find the other factor. $$ 6 b^{2}-6 b-3,3 $$

In the following problems, the first quantity represents the product and the second quantity represents a factor of that product. Find the other factor. $$ 12 a^{3} b^{2} c^{8}, 12 a^{3} b^{2} c^{8} $$

For the following problems, factor the binomials. $$ 121 a^{2}-9 $$

For the following problems, factor the trinomials when possible. $$ y^{2}-4 y-32 $$

Factor the following problems, if possible. $$ 16 y^{2}-26 y+3 $$

For the following problems, use the grouping method to factor the polynomials. Some polynomials may not. be factorable using the grouping method. $$ a^{3} b^{2} c d+a b c^{2} d x-a^{2} b x y-c x^{2} y $$

For the following problems, the first quantity represents the product and the second quantity a factor. Find the other factor. $$ 18 x^{3}+20 x, 2 x $$

For the following problems, factor the polynomials. $$ 12 x^{2}-8 x-16 $$

For the following problems, factor the polynomials. $$ 15 y^{3}-24 y+9 $$

For the following problems, factor the binomials. $$ 12 a^{2}-75 $$