Chapter 6

Determine whether each trinomial is a perfect square trinomial. $$ x^{2}+16 x+64 $$

Represent each given condition using a single variable, \(x\). The length and width of a rectangle whose length 4 centimeters more than its width

Factor each polynomial by grouping. Notice that Step 3 has already been done in these exercises. $$ x^{2}+3 x+2 x+6 $$

Find the \(G C F\) for each list. $$ 32,36 $$

Factor each trinomial completely. If a polynomial can't be factored, write "prime." $$ x^{2}+7 x+6 $$

Solve each equation. $$ (x-2)(x+1)=0 $$

Determine whether each trinomial is a perfect square trinomial. $$ x^{2}+22 x+121 $$

Represent each given condition using a single variable, \(x\). The length and width of a rectangle whose length is twice its width

Factor each polynomial by grouping. Notice that Step 3 has already been done in these exercises. $$ x^{2}+5 x+3 x+15 $$

Find the \(G C F\) for each list. $$ 36,90 $$

Factor each trinomial completely. If a polynomial can't be factored, write "prime." $$ x^{2}+6 x+8 $$

Solve each equation. $$ (x+3)(x+2)=0 $$

Represent each given condition using a single variable, \(x\). Two consecutive odd integers

Factor each polynomial by grouping. Notice that Step 3 has already been done in these exercises. $$ y^{2}+8 y-2 y-16 $$

Find the \(G C F\) for each list. $$ 18,42,84 $$

Factor each trinomial completely. If a polynomial can't be factored, write "prime." $$ y^{2}-10 y+9 $$

Solve each equation. $$ (x-6)(x-7)=0 $$

Factor each polynomial by grouping. Notice that Step 3 has already been done in these exercises. $$ z^{2}+10 z-7 z-70 $$

Find the \(G C F\) for each list. $$ 30,75,135 $$

Factor each trinomial completely. If a polynomial can't be factored, write "prime." $$ y^{2}-12 y+11 $$

Solve each equation. $$ (x+4)(x-10)=0 $$

Determine whether each trinomial is a perfect square trinomial. $$ 4 x^{2}+12 x y+8 y^{2} $$

Represent each given condition using a single variable, \(x\). The base and height of a triangle whose height is one more than four times its base

Factor each polynomial by grouping. Notice that Step 3 has already been done in these exercises. $$ 8 x^{2}-5 x-24 x+15 $$

Find the \(G C F\) for each list. $$ 24,14,21 $$

Factor each trinomial completely. If a polynomial can't be factored, write "prime." $$ x^{2}-6 x+9 $$

Solve each equation. $$ (x+9)(x+17)=0 $$

Determine whether each trinomial is a perfect square trinomial. $$ 25 x^{2}+20 x y+2 y^{2} $$

Represent each given condition using a single variable, \(x\). The base and height of a trapezoid whose base is three less than five times its height

Factor each polynomial by grouping. Notice that Step 3 has already been done in these exercises. $$ 4 x^{2}-9 x-32 x+72 $$

Find the \(G C F\) for each list. $$ 15,25,27 $$

Factor each trinomial completely. If a polynomial can't be factored, write "prime." $$ x^{2}-10 x+25 $$

Solve each equation. $$ (x-11)(x-1)=0 $$

Determine whether each trinomial is a perfect square trinomial. $$ 25 a^{2}-40 a b+16 b^{2} $$

Use the information given to find the dimensions of each figure. The area of the square is 121 square units. Find the length of its sides.

Factor each polynomial by grouping. Notice that Step 3 has already been done in these exercises. $$ 5 x^{4}-3 x^{2}+25 x^{2}-15 $$

Find the \(G C F\) for each list. $$ y^{2}, y^{4}, y^{7} $$

Factor each trinomial completely. If a polynomial can't be factored, write "prime." $$ x^{2}-3 x-18 $$

Factor each trinomial completely. See Examples 1 through 5 . \(2 x^{2}+13 x+15\)

Solve each equation. $$ x(x+6)=0 $$

Determine whether each trinomial is a perfect square trinomial. $$ 36 a^{2}-12 a b+b^{2} $$

Factor each polynomial by grouping. Notice that Step 3 has already been done in these exercises. $$ 2 y^{4}-10 y^{2}+7 y^{2}-35 $$

Find the \(G C F\) for each list. $$ x^{3}, x^{2}, x^{5} $$

Factor each trinomial completely. If a polynomial can't be factored, write "prime." $$ x^{2}-x-30 $$

Solve each equation. $$ x(x-7)=0 $$

Determine whether each trinomial is a perfect square trinomial. $$ m^{2}-2 m+1 $$

Factor each trinomial by grouping. Exercises 9 through 12 are broken into parts to help you get started. \(6 x^{2}+11 x+3\) a. Find two numbers whose product is \(6 \cdot 3=18\) and whose sum is 11 b. Write \(11 x\) using the factors from part (a). c. Factor by grouping.

Find the \(G C F\) for each list. $$ z^{7}, z^{9}, z^{11} $$

Factor each trinomial completely. If a polynomial can't be factored, write "prime." $$ x^{2}+3 x-70 $$

Factor each trinomial completely. See Examples 1 through 5 . \(8 y^{2}-17 y+9\)