Chapter 6

Factor out the GCF from each polynomial. $$ 3 a+6 $$

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. $$ 2 x^{3}-18 x^{2}+40 x $$

Factor each trinomial completely. See Examples 1 through 5 . \(2 x^{2}-7 x-99\)

Solve. $$ x^{2}+20 x=0 $$

Factor each trinomial completely. $$ 25 x^{2}-60 x y+36 y^{2} $$

Factor each trinomial by grouping. Exercises 9 through 12 are broken into parts to help you get started. $$ 21 x^{2}-13 x+2 $$

Factor out the GCF from each polynomial. $$ 18 a+12 $$

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. $$ 3 x^{3}-12 x^{2}-36 x $$

Factor each trinomial completely. See Examples 1 through 5 . \(2 x^{2}+7 x-72\)

Solve. $$ x^{2}+15 x=0 $$

Factor each trinomial completely. $$ x^{4}+4 x^{2}+4 $$

If the sides of a square are increased by 3 inches, the area becomes 64 square inches. Find the length of the sides of the original square.

Factor each trinomial by grouping. Exercises 9 through 12 are broken into parts to help you get started. $$ 2 x^{3}+13 x^{2}+15 x $$

Factor out the GCF from each polynomial. $$ 30 x-15 $$

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 5 . \(-27 t+7 t^{2}-4\)

Solve. $$ x^{2}=16 $$

Factor each trinomial completely. $$ m^{4}+10 m^{2}+25 $$

If the sides of a square are increased by 5 meters, the area becomes 100 square meters. Find the length of the sides of the original square.

Factor each trinomial by grouping. Exercises 9 through 12 are broken into parts to help you get started. $$ 3 x^{3}+8 x^{2}+4 x $$

Factor out the GCF from each polynomial. $$ 42 x-7 $$

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. $$ x^{2}-4 x y-77 y^{2} $$

Factor each trinomial completely. See Examples 1 through 5 . \(-3 t+4 t^{2}-7\)

Solve. $$ x^{2}=9 $$

Factor each completely. \(x^{2}-25\)

One leg of a right triangle is 4 millimeters longer than the smaller leg and the hypotenuse is 8 millimeters longer than the smaller leg. Find the lengths of the sides of the triangle.

Factor each trinomial by grouping. Exercises 9 through 12 are broken into parts to help you get started. $$ 16 y^{2}-34 y+18 $$

Factor out the GCF from each polynomial. $$ x^{3}+5 x^{2} $$

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. $$ x^{2}+15 x+36 $$

Factor each trinomial completely. See Examples 1 through 5 . \(3 a^{2}+10 a b+3 b^{2}\)

Solve. $$ x^{2}-4 x=32 $$

Factor each completely. $$ y^{2}-100 $$

One leg of a right triangle is 9 centimeters longer than the other leg and the hypotenuse is 45 centimeters. Find the lengths of the legs of the triangle.

Factor each trinomial by grouping. Exercises 9 through 12 are broken into parts to help you get started. $$ 4 y^{2}-2 y-12 $$

Factor out the GCF from each polynomial. $$ y^{5}+6 y^{4} $$

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. $$ x^{2}+19 x+60 $$

Factor each trinomial completely. See Examples 1 through 5 . \(2 a^{2}+11 a b+5 b^{2}\)

Solve. $$ x^{2}-5 x=24 $$

Factor each completely. $$ 9-4 z^{2} $$

The length of the base of a triangle is twice its height. If the area of the triangle is 100 square kilometers, find the height.

Factor each trinomial by grouping. Exercises 9 through 12 are broken into parts to help you get started. $$ -13 x+6+6 x^{2} $$

Factor out the GCF from each polynomial. $$ 6 y^{4}+2 y^{3} $$

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. $$ x^{2}-x-2 $$

Solve. $$ (x+4)(x-9)=4 x $$

Factor each completely. $$ 16 x^{2}-y^{2} $$

The height of a triangle is 2 millimeters less than the base. If the area is 60 square millimeters, find the base.

Factor each trinomial by grouping. Exercises 9 through 12 are broken into parts to help you get started. $$ -25 x+12+12 x^{2} $$

Factor out the GCF from each polynomial. $$ 5 x^{2}+10 x^{6} $$

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. $$ x^{2}-5 x-14 $$

Factor each trinomial completely. See Examples 1 through 5 . \(3 r^{2}+10 r-8\)