Chapter 6

Factor the following problems, if possible. $$ 6 a^{2}+13 a+6 $$

For the following problems, the first quantity represents the product and the second quantity a factor. Find the other factor. $$ 9 a^{5}+6 a^{5}-18 a^{4}+24 a^{2}, \quad 3 a^{2} $$

For the following problems, factor the polynomials. $$ -6 y^{3}-8 y^{2}-14 y+10 $$

Simplify \(\left(x^{4} y^{0} z^{2}\right)^{3}\)

For the following problems, use the grouping method to factor the polynomials. Some may not be factorable. $$ 8 a^{2} b c+20 a^{2} b c+10 a^{3} b^{3} c+25 a^{3} b^{3} $$

For the following problems, factor the trinomials when possible. $$ 6 x^{2}-54 x+48 $$

For the following problems, factor the binomials. $$ 16 x^{2}-25 y^{2} $$

For the following problems, the first quantity represents the product and the second quantity a factor. Find the other factor. $$ 10 x^{3}-35 x^{2}, \quad 5 x^{2} $$

For the following problems, factor the polynomials. $$ A b+A c $$

Simplify \(-\\{-[-(-|6|)]\\}\).

For the following problems, use the grouping method to factor the polynomials. Some may not be factorable. $$ a(a+6)-(a+6)+a(a-4)-(a-4) $$

For the following problems, factor the trinomials when possible. $$ x^{3}+6 x^{2}+8 x $$

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

For the following problems, the first quantity represents the product and the second quantity a factor. Find the other factor. $$ 12 x^{3} y^{5}+20 x^{3} y^{2}, \quad 4 x^{3} y^{2} $$

For the following problems, factor the polynomials. $$ N x+N y $$

Find the product. \((2 x-4)^{2}\).

For the following problems, use the grouping method to factor the polynomials. Some may not be factorable. $$ a(2 x+7)-4(2 x+7)+a(x-10)-4(x-10) $$

For the following problems, factor the trinomials when possible. $$ x^{3}-8 x^{2}+15 x $$

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

For the following problems, the given trinomial occurs when solving the corresponding applied problem. Factor each trinomial. You do not need to solve the problem. \(5 r^{2}-24 r-5\) It takes 5 hours to paddle a boat 12 miles downstream and then back. The current flows at the rate of 1 mile per hour. At what rate was the boat paddled?

For the following problems, the first quantity represents the product and the second quantity a factor. Find the other factor. $$ 10 a^{4} b^{3}+4 a^{3} b^{4}, \quad 2 a^{3} b^{3} $$

For the following problems, factor the polynomials. $$ Q x+Q y $$

For the following problems, factor the polynomials. $$ A x-A y $$

For the following problems, factor the trinomials when possible. $$ x^{4}+9 x^{3}+14 x^{2} $$

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

For the following problems, the given trinomial occurs when solving the corresponding applied problem. Factor each trinomial. You do not need to solve the problem. \(x^{2}+5 x-84\) The length of a rectangle is 5 inches more than the width of the rectangle. If the area of the rectangle is 84 square inches, what are the length and width of the rectangle?

For the following problems, the first quantity represents the product and the second quantity a factor. Find the other factor. $$ 8 a^{3} b^{6} c^{8}+12 a^{2} b^{5} c^{6}-16 a^{2} b^{7} c^{5}, \quad 4 a^{2} b^{5} c^{5} $$

For the following problems, factor the polynomials. $$ (x+4) b+(x+4) c $$

For the following problems, factor the trinomials when possible. $$ 2 a^{3}+12 a^{2}+10 a $$

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

For the following problems, the given trinomial occurs when solving the corresponding applied problem. Factor each trinomial. You do not need to solve the problem. \(x^{2}+24 x-145\) A square measures 12 inches on each side. Another square is to be drawn around this square in such a way that the total area is 289 square inches. What is the distance from the edge of the smaller square to the edge of the larger square? (The two squares have the same center.)

For the following problems, factor the trinomials when possible. $$ 4 a^{3}-40 a^{2}+84 a $$

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

For the following problems, the first quantity represents the product and the second quantity a factor. Find the other factor. $$ 14 a^{5} b^{2}-3 a^{4} b^{4}+7 a^{3}, a^{3} $$

For the following problems, factor the polynomials. $$ (x-9) a+(x-9) b $$

For the following problems, factor the trinomials if possible. $$ 16 x^{2}-8 x y-3 y^{2} $$

For the following problems, factor the polynomials. $$ (2 x+7) a+(2 x+7) b $$

For the following problems, factor the binomials. $$ b^{6}-y^{2} $$

For the following problems, the first quantity represents the product and the second quantity a factor. Find the other factor. $$ 64 a^{5} b^{3} c^{11}+56 a^{4} b^{4} c^{10}-48 a^{3} b^{5} c^{9}-8 a^{3} b^{2} c^{5}, \quad 8 a^{3} b^{2} c^{5} $$

For the following problems, factor the trinomials if possible. $$ 6 a^{2}+7 a b+2 b^{2} $$

For the following problems, factor the polynomials. $$ (9 a-b) w-(9 a-b) x $$

For the following problems, factor the binomials. $$ b^{6}-x^{4} $$

For the following problems, the first quantity represents the product and the second quantity a factor. Find the other factor. $$ 3 h^{3} b^{2}-2 h^{6} b^{3}-9 h^{2} b+h b, \quad h b $$

For the following problems, factor the trinomials if possible. $$ 12 a^{2}+7 a b+12 b^{2} $$

For the following problems, factor the polynomials. $$ (5-v) X+(5-v) Y $$

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

For the following problems, the first quantity represents the product and the second quantity a factor. Find the other factor. $$ 5 a+10,-5 $$

For the following problems, factor the trinomials if possible. $$ 9 x^{2}+18 x y+8 y^{2} $$

For the following problems, factor the polynomials, if possible. $$ a^{2}+9 a+20 $$

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