Chapter 6

For the following problems, factor the trinomials when possible. $$ x^{2}+13 x+42 $$

Factor the following problems, if possible. $$ 3 y^{2}+14 y-5 $$

For the following problems, use the grouping method to factor the polynomials. Some polynomials may not. be factorable using the grouping method. $$ 5 m^{10} n^{17} p^{3}-m^{6} n^{7} p^{4}-40 m^{4} n^{10} q t^{2}+8 p q t^{2} $$

For the following problems, the first quantity represents the product and the second quantity a factor. Find the other factor. $$ 40 y^{3}+24 y, \quad 4 y $$

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

For the following problems, factor the trinomials when possible. $$ x^{2}+2 x-35 $$

For the following problems, factor the binomials. $$ 10 y^{2}-320 $$

Factor the following problems, if possible. $$ 10 x^{2}+29 x+10 $$

For the following problems, the first quantity represents the product and the second quantity a factor. Find the other factor. $$ 16 x^{3}-12 x^{2}, \quad 4 x^{2} $$

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

In the following problems, the first quantity represents the product and the second quantity represents a factor of that product. Find the other factor. $$ 14(a-3)^{6}(a+4)^{2}, \quad 2(a-3)^{2}(a+4) $$

For the following problems, factor the polynomials. $$ b y^{3}+b y^{2}+b y+b $$

For the following problems, factor the trinomials when possible. $$ x^{2}+13 x+40 $$

For the following problems, factor the binomials. $$ 8 y^{2}-50 $$

Factor the following problems, if possible. $$ 14 y^{2}+29 y-15 $$

For the following problems, the first quantity represents the product and the second quantity a factor. Find the other factor. $$ 11 x^{3}-11 x+11, \quad 11 $$

In the following problems, the first quantity represents the product and the second quantity represents a factor of that product. Find the other factor. $$ 26(x-5 y)^{10}(x-3 y)^{12}, \quad-2(x-5 y)^{7}(x-3 y)^{7} $$

For the following problems, use the grouping method to factor the polynomials. Some may not be factorable. $$ 4 a x+x+4 a y+y $$

For the following problems, factor the trinomials when possible. $$ y^{2}+6 y-27 $$

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

For the following problems, the first quantity represents the product and the second quantity a factor. Find the other factor. $$ 10 a^{3}+12 a^{2}+16 a+8, \quad 2 $$

For the following problems, factor the polynomials. $$ 2 y^{2}+6 y+4 x y $$

In the following problems, the first quantity represents the product and the second quantity represents a factor of that product. Find the other factor. $$ 34(1-a)^{4}(1+a)^{8}-17(1-a)^{4}(1+a)^{2} $$

For the following problems, use the grouping method to factor the polynomials. Some may not be factorable. $$ x y+4 x-3 y-12 $$

For the following problems, factor the trinomials when possible. $$ b^{2}+15 b+56 $$

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

For the following problems, factor the polynomials. $$ 9 x^{2}+6 x y+4 x $$

In the following problems, the first quantity represents the product and the second quantity represents a factor of that product. Find the other factor. $$ (x+y)(x-y), \quad x-y $$

For the following problems, use the grouping method to factor the polynomials. Some may not be factorable. $$ 2 a b-8 b-3 a b-12 a $$

For the following problems, factor the trinomials when possible. $$ 3 a^{2}+24 a+36 $$

For the following problems, factor the binomials. $$ x^{4} y^{4}-36 $$

Factor the following problems, if possible. $$ 24 x^{2}-34 x+5 $$

For the following problems, the first quantity represents the product and the second quantity a factor. Find the other factor. $$ 8 a^{3}-4 a^{2}-12 a+16, \quad 4 $$

For the following problems, factor the polynomials. $$ 30 a^{2} b^{2}+40 a^{2} b^{2}+50 a^{2} b^{2} $$

In the following problems, the first quantity represents the product and the second quantity represents a factor of that product. Find the other factor. $$ (a+3)(a-3), \quad a-3 $$

For the following problems, factor the trinomials when possible. $$ 4 x^{2}+12 x+8 $$

For the following problems, use the grouping method to factor the polynomials. Some may not be factorable. $$ a^{2}-7 a+a b-7 b $$

For the following problems, factor the binomials. $$ x^{4} y^{4}-9 a^{2} $$

Factor the following problems, if possible. $$ 24 x^{2}-26 x-5 $$

For the following problems, factor the polynomials. $$ 13 x^{2} y^{5} c-26 x^{2} y^{5} c-39 x^{2} y^{5} $$

For the following problems, use the grouping method to factor the polynomials. Some may not be factorable. $$ m^{2}+5 m+n m+5 n $$

For the following problems, factor the trinomials when possible. $$ 2 a^{2}-18 a+40 $$

For the following problems, factor the binomials. $$ a^{2} b^{4}-16 y^{4} $$

Factor the following problems, if possible. $$ 24 x^{2}+26 x-5 $$

For the following problems, the first quantity represents the product and the second quantity a factor. Find the other factor. $$ 4 x^{6}+16 x^{4}-16 x, \quad 4 x $$

For the following problems, factor the polynomials. $$ -4 x^{2}-12 x-8 $$

In the following problems, the first quantity represents the product and the second quantity represents a factor of that product. Find the other factor. $$ 0.0024 x^{4 n} y^{3 n+5} z^{2}, 0.03 x^{3 n} y^{5} $$

For the following problems, use the grouping method to factor the polynomials. Some may not be factorable. $$ r^{2}+r s-r-s $$

For the following problems, factor the trinomials when possible. $$ 5 y^{2}-70 y+440 $$

For the following problems, factor the binomials. $$ 4 a^{2} b^{2}-9 b^{2} $$