Chapter 6

Factor out the GCF from each polynomial. $$ x\left(y^{2}+1\right)-3\left(y^{2}+1\right) $$

Factor each trinomial completely. Some of these trinomials contain a greatest common factor (other than 1). Don't forget to factor out the GCF first. $$ 3 x^{3}+3 x^{2}-126 x $$

Factor each trinomial completely. See Examples 1 through 7. \(6 x^{2}-11 x-10\)

Solve each equation. $$ x^{2}-26=-11 x $$

Factor each completely. $$ x^{2}+16 x+64-x^{4} $$

Factor each trinomial by grouping. Exercises 9 through 12 are broken into parts to help you get started. $$ 6-11 x+5 x^{2} $$

Factor out the GCF from each polynomial. $$ z(y+4)+3(y+4) $$

Factor each trinomial completely. Some of these trinomials contain a greatest common factor (other than 1). Don't forget to factor out the GCF first. $$ 4 x^{2} y+4 x y-12 y $$

Factor each trinomial completely. See Examples 1 through 7. \(3 x^{2}-42 x+63\)

Solve each equation. $$ 30 x^{2}-11 x=30 $$

Factor each completely. $$ x^{2}+20 x+100-x^{4} $$

Two boats travel at right angles to each other after leaving the same dock at the same time. One hour later the boats are 17 miles apart. If one boat travels 7 miles per hour faster than the other boat, find the rate of each boat.

Factor each trinomial by grouping. Exercises 9 through 12 are broken into parts to help you get started. $$ 5-12 x+7 x^{2} $$

Factor out the GCF from each polynomial. $$ 8(x+2)-y(x+2) $$

Factor each trinomial completely. Some of these trinomials contain a greatest common factor (other than 1). Don't forget to factor out the GCF first. $$ 3 x^{2} y-9 x y+45 y $$

Factor each trinomial completely. See Examples 1 through 7. \(5 x^{2}-75 x+60\)

Solve each equation. $$ 9 x^{2}+7 x=2 $$

Factor each completely. $$ x^{2}-10 x+25-y^{2} $$

The side of a square equals the width of a rectangle. The length of the rectangle is 6 meters longer than its width. The sum of the areas of the square and the rectangle is 176 square meters. Find the side of the square.

Multiply. $$ (x-2)(x+2) $$

Factor out the GCF from each polynomial. $$ r\left(z^{2}-6\right)+\left(z^{2}-6\right) $$

Factor each trinomial completely. Some of these trinomials contain a greatest common factor (other than 1). Don't forget to factor out the GCF first. $$ x^{2}-4 x-21 $$T

Factor each trinomial completely. See Examples 1 through 7. \(8 x^{2}+6 x y-27 y^{2}\)

Solve each equation. $$ 5 x^{2}-6 x-8=0 $$

Factor each completely. $$ x^{2}-18 x+81-y^{2} $$

The sum of two numbers is 20 , and the sum of their squares is 218 . Find the numbers.

Multiply. $$ (y-5)(y+5) $$

Factor out the GCF from each polynomial. $$ q\left(b^{3}-5\right)+\left(b^{3}-5\right) $$

Factor each trinomial completely. Some of these trinomials contain a greatest common factor (other than 1). Don't forget to factor out the GCF first. $$ x^{2}-4 x-32 $$

Factor each trinomial completely. See Examples 1 through 7. \(54 a^{2}+39 a b-8 b^{2}\)

Solve each equation. $$ 12 x^{2}+7 x-12=0 $$

Factor each completely. $$ 4 x^{2}+4 x+1-z^{2} $$

The sum of two numbers is \(25,\) and the sum of their squares is \(325 .\) Find the numbers.

Multiply. $$ (y+4)(y+4) $$

Factor \(a\) "-1" from each polynomial. $$ -x-7 $$

Factor each trinomial completely. Some of these trinomials contain a greatest common factor (other than 1). Don't forget to factor out the GCF first. $$ x^{2}+7 x y+10 y^{2} $$

Factor each trinomial completely. See Examples 1 through 7. \(-x^{2}+2 x+24\)

Solve each equation. $$ 6 y^{2}-22 y-40=0 $$

Factor each completely. $$ 9 y^{2}+12 y+4-x^{2} $$

A rectangular garden is surrounded by a walk of uniform width. The area of the garden is 180 square yards. If the dimensions of the garden plus the walk are 16 yards by 24 yards, find the width of the walk.

Multiply. $$ (x+7)(x+7) $$

Factor \(a\) "-1" from each polynomial. $$ -y-3 $$

Factor each trinomial completely. Some of these trinomials contain a greatest common factor (other than 1). Don't forget to factor out the GCF first. $$ x^{2}-3 x y-4 y^{2} $$

Factor each trinomial completely. See Examples 1 through 7. \(-x^{2}+4 x+21\)

Solve each equation. $$ 3 x^{2}-6 x-9=0 $$

Factor each completely. $$ m^{4}-1 $$

A rectangular pool is surrounded by a walk 4 meters wide. The pool is 6 meters longer than its width. If the total area of the pool and walk is 576 square meters more than the area of the pool, find the dimensions of the pool.

Multiply. $$ (9 z+5)(9 z-5) $$

Factor \(a\) "-1" from each polynomial. $$ -2+z $$

Factor each trinomial completely. Some of these trinomials contain a greatest common factor (other than 1). Don't forget to factor out the GCF first. $$ 64+24 t+2 t^{2} $$