Chapter 6

Factor each trinomial completely. See Examples 1 through 7. \(4 x^{3}-9 x^{2}-9 x\)

Solve each equation. $$ (y-2)(y+3)=6 $$

Factor each completely. $$ n^{4}-16 $$

According to the International America's Cup Class (IACC) rule, a sailboat competing in the America's Cup match must have a 110 -foot-tall mast and a combined mainsail and jib sail area of 3000 square feet. (Source: America's Cup Organizing Committee) A design for an IACC-class sailboat calls for the mainsail to be \(60 \%\) of the combined sail area. If the height of the triangular mainsail is 28 feet more than twice the length of the boom, find the length of the boom and the height of the mainsail.

Multiply. $$ (8 y+9)(8 y-9) $$

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. $$ 50+20 t+2 t^{2} $$

Factor each trinomial completely. See Examples 1 through 7. \(6 x^{3}-31 x^{2}+5 x\)

Solve each equation. $$ (y-5)(y-2)=28 $$

Factor. $$ x^{3}+27 $$

Multiply. $$ (4 x-3)^{2} $$

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. $$ x^{3}-2 x^{2}-24 x $$

Factor each trinomial completely. See Examples 1 through 7. \(24 x^{2}-58 x+9\)

Solve each equation. $$ x^{3}-12 x^{2}+32 x=0 $$

Factor. $$ y^{3}+1 $$

Factor \(a\) "-1" from each polynomial. $$ 2 y-z-11 $$

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. $$ x^{3}-3 x^{2}-28 x $$

Factor each trinomial completely. See Examples 1 through 7. \(36 x^{2}+55 x-14\)

Solve each equation. $$ x^{3}-14 x^{2}+49 x=0 $$

Factor. $$ z^{3}-1 $$

Factor each four-term polynomial by grouping. If this is not possible, write "not factorable by grouping." $$ x^{3}+2 x^{2}+5 x+10 $$

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. $$ 2 t^{5}-14 t^{4}+24 t^{3} $$

Factor each trinomial completely. See Examples 1 through 7. \(40 a^{2} b+9 a b-9 b\)

Solve each equation. $$ x^{2}+14 x+49=0 $$

Factor. $$ 8-z^{3} $$

Factor each four-term polynomial by grouping. If this is not possible, write "not factorable by grouping." $$ x^{3}+4 x^{2}+3 x+12 $$

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. $$ 3 x^{6}+30 x^{5}+72 x^{4} $$

Factor each trinomial completely. See Examples 1 through 7. \(24 y^{2} x+7 y x-5 x\)

Solve each equation. $$ x^{2}+22 x+121=0 $$

Factor. $$ m^{3}+n^{3} $$

Factor each polynomial by grouping. $$ \begin{aligned} &x^{2 n}+2 x^{n}+3 x^{n}+6\\\ &\text { (Hint: Don't forget that } \left.x^{2 n}=x^{n} \cdot x^{n} .\right) \end{aligned} $$

Factor each four-term polynomial by grouping. If this is not possible, write "not factorable by grouping." $$ 5 x+15+x y+3 y $$

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. $$ 5 x^{3} y-25 x^{2} y^{2}-120 x y^{3} $$

Factor each trinomial completely. See Examples 1 through 7. \(30 x^{3}+38 x^{2}+12 x \quad\) 62. \(6 x^{3}-28 x^{2}+16 x\)

Solve each equation. $$ 12 y=8 y^{2} $$

Factor. $$ r^{3}+125 $$

Factor each polynomial by grouping. $$ x^{2 n}+6 x^{n}+10 x^{n}+60 $$

Factor each four-term polynomial by grouping. If this is not possible, write "not factorable by grouping." $$ x y+y+2 x+2 $$

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. $$ 7 a^{3} b-35 a^{2} b^{2}+42 a b^{3} $$

Factor each trinomial completely. See Examples 1 through 7. \(30 x^{3}+38 x^{2}+12 x \quad\) 62. \(6 x^{3}-28 x^{2}+16 x\)

Solve each equation. $$ 9 y=6 y^{2} $$

Factor. $$ x^{3} y^{2}-27 y^{2} $$

Factor each four-term polynomial by grouping. If this is not possible, write "not factorable by grouping." $$ 6 x^{3}-4 x^{2}+15 x-10 $$

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. $$ 162-45 m+3 m^{2} $$

Factor each trinomial completely. See Examples 1 through 7. \(6 y^{3}-8 y^{2}-30 y\)

Solve each equation. $$ 7 x^{3}-7 x=0 $$

Factor. $$ 64-p^{3} $$

Factor each polynomial by grouping. $$ 12 x^{2 n}-40 x^{n}+25 $$

Factor each four-term polynomial by grouping. If this is not possible, write "not factorable by grouping." $$ 16 x^{3}-28 x^{2}+12 x-21 $$

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. $$ 48-20 n+2 n^{2} $$

Factor each trinomial completely. See Examples 1 through 7. \(12 x^{3}-34 x^{2}+24 x\)