Chapter 6

For the following problems, the first quantity represents the product and the second quantity represents a factor. Find the other factor. $$ 32 a^{4} b, \quad 2 b $$

The product is \(27 a^{3}+9 a^{2}+9 a\) and a factor is \(3 a\). Find the other factor.

Factor the following, if possible. $$ 2 x^{2}+13 x-7 $$

Factor, if possible, the following trinomials. \(k^{2}+8 k+15\)

If possible, factor the following binomials completely. $$ m^{2}-25 $$

Use the grouping method to factor the following polynomials. $$ a x+a y+b x+b y $$

Factor \(4 x-48\).

The product is \(3 x^{2}-6 x\) and a factor is \(3 x\). Find the other factor.

The product is 84 and one factor is 6. What is the other factor?

For the following problems, the first quantity represents the product and the second quantity represents a factor. Find the other factor. $$ 35 x^{3} y^{2}, \quad 7 x^{3} $$

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

Factor, if possible, the following trinomials. \(y^{2}+7 y-30\)

If possible, factor the following binomials completely. $$ 36 p^{2}-81 q^{2} $$

Use the grouping method to factor the following polynomials. $$ 2 a m+8 m+5 a n+20 n $$

Factor \(6 y^{3}+24 y^{2}+36 y\).

The product is \(5 y^{2}+10 y^{3}-15 y^{2}\) and a factor is \(5 y^{2}\), Find the other factor.

The product is \(14 x^{3} y^{2} z^{5}\) and one factor is \(7 x y z\). What is the other factor?

For the following problems, the first quantity represents the product and the second quantity represents a factor. Find the other factor. $$ 44 a^{2} b^{2} c, \quad 11 b^{2} $$

For the following problems, factor, if possible, the polynomials. $$ -14 x^{2} y^{4} b-28 x^{2} y^{3} b-42 x^{2} y^{2} $$

Factor the following, if possible. $$ 4 a^{2}-25 a-21 $$

Factor, if possible, the following trinomials. \(m^{2}+10 m+24\)

If possible, factor the following binomials completely. $$ 49 a^{4}-b^{2} c^{2} $$

Use the grouping method to factor the following polynomials. $$ a^{2} x^{3}+4 a^{2} y^{3}+3 b x^{3}+12 b y^{3} $$

The product is \(4 x^{5} y^{3}-8 x^{4} y^{4}+16 x^{3} y^{5}+24 x y^{7}\) and a factor is \(4 x y^{3}\). Find the other factor.

Factor \(10 a^{5} b^{4}-14 a^{4} b^{5}-8 b^{6}\).

In the following problems, the first quantity represents the product and the second quantity represents a factor of that product. Find the other factor. 30,6

For the following problems, the first quantity represents the product and the second quantity represents a factor. Find the other factor. $$ 50 m^{3} n^{5} p^{4} q, \quad 10 m^{3} q $$

For the following problems, factor, if possible, the polynomials. $$ (y+2) a+(y+2) c $$

Factor the following, if possible. $$ 16 b^{2}-22 b-3 $$

Factor, if possible, the following trinomials. \(m^{2}-10 m+16\)

If possible, factor the following binomials completely. $$ x^{8} y^{4}-100 w^{12} $$

Use the grouping method to factor the following polynomials. $$ 15 m x+10 n x-6 m y-4 n y $$

The product is \(-25 a^{4}-35 a^{2}+5\) and a factor is \(-5 .\) Find the other factor.

Factor \(-14 m^{4}+28 m^{2}-7 m\).

In the following problems, the first quantity represents the product and the second quantity represents a factor of that product. Find the other factor. 45,9

For the following problems, the first quantity represents the product and the second quantity represents a factor. Find the other factor. $$ 51(a+1)^{2}(b+3)^{4}, \quad 3(a+1) $$

For the following problems, factor, if possible, the polynomials. $$ 6 x^{2} y^{2} z+5 x^{2} y^{3}-12 x y z-10 x y^{2} $$

Factor the following, if possible. $$ 10 y^{2}-19 y-15 $$

Factor, if possible, the following trinomials. \(4 k^{2}+32 k+28\)

Use the grouping method to factor the following polynomials. $$ 40 a b x-24 a b x y-35 c^{2} x+21 c^{2} x y $$

The product is \(-a^{2}+b^{2}\) and a factor is -1 . Find the other factor.

Factor \((y+4) a+(y+4) b\).

In the following problems, the first quantity represents the product and the second quantity represents a factor of that product. Find the other factor. $$ 10 a, 5 $$

For the following problems, the first quantity represents the product and the second quantity a factor. Find the other factor. $$ 4 x+10,2 $$

For the following problems, factor, if possible, the polynomials. $$ 4 a^{2}-16 c^{2} $$

Factor, if possible, the following trinomials. \(3 y^{4}+24 y^{3}+36 y^{2}\)

Factor the following, if possible. $$ 6 m^{3}+40 m^{2}-14 m $$

Use the grouping method to factor the following polynomials. When factoring the polynomial \(8 a^{2} b^{4}-4 b^{4}+14 a^{2}-7\) in Sample Set A, we grouped together terms 1 and 2 and 3 and 4 . Could we have grouped together terms 1 and 3 and 2 and \(4 ?\) Try this. \(8 a^{2} b^{4}-4 b^{4}+14 a^{2}-7=\)

Factor \(8 m^{3}(n-4)-6 m^{2}(n-4)\).

In the following problems, the first quantity represents the product and the second quantity represents a factor of that product. Find the other factor. $$ 16 a, 8 $$