Chapter 6

Solve each equation. $$ 3 x^{3}-27 x=0 $$

Factor. $$ a^{3} b+8 b^{4} $$

Factor each four-term polynomial by grouping. If this is not possible, write "not factorable by grouping." $$ 5 m^{3}+6 m n+5 m^{2}+6 n $$

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. $$ \begin{aligned} &-x^{2}+12 x-11\\\ &\text { (Factor out }-1 \text { first.) } \end{aligned} $$

Factor each trinomial completely. See Examples 1 through 7. \(10 x^{4}+25 x^{3} y-15 x^{2} y^{2}\)

Solve each equation. $$ 3 x^{2}+8 x-11=13-6 x $$

Factor. $$ 8 a b^{3}+27 a^{4} $$

Factor each four-term polynomial by grouping. If this is not possible, write "not factorable by grouping." $$ 8 w^{2}+7 w v+8 w+7 v $$

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. $$ \begin{aligned} &-x^{2}+8 x-7\\\ &\text { Factor out }-1 \text { first.) } \end{aligned} $$

Factor each trinomial completely. See Examples 1 through 7. \(42 x^{4}-99 x^{3} y-15 x^{2} y^{2}\)

Solve each equation. $$ 2 x^{2}+12 x-1=4+3 x $$

Factor. $$ 125 y^{3}-8 x^{3} $$

Factor each four-term polynomial by grouping. If this is not possible, write "not factorable by grouping." $$ 2 y-8+x y-4 x $$

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. $$ \begin{aligned} &\frac{1}{2} y^{2}-\frac{9}{2} y-11\\\ &\text { (Factor out } \frac{1}{2} \text { first.) } \end{aligned} $$

Factor each trinomial completely. See Examples 1 through 7. \(-14 x^{2}+39 x-10\)

Solve each equation. $$ 3 x^{2}-20 x=-4 x^{2}-7 x-6 $$

Factor. $$ 54 y^{3}-128 $$

Multiply. $$ (2 z-1)^{2} $$

Factor each four-term polynomial by grouping. If this is not possible, write "not factorable by grouping." $$ 6 x-42+x y-7 y $$

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. $$ \frac{1}{3} y^{2}-\frac{5}{3} y-8 $$ $$ \text { (Factor out } \frac{1}{3} \text { first.) } $$

Factor each trinomial completely. See Examples 1 through 7. \(-15 x^{2}+26 x-8\)

Solve each equation. $$ 4 x^{2}-20 x=-5 x^{2}-6 x-5 $$

Factor. $$ x^{6}-y^{3} $$

Factor each four-term polynomial by grouping. If this is not possible, write "not factorable by grouping." $$ 2 x^{3}+x^{2}+8 x+4 $$

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. $$ x^{3} y^{2}+x^{2} y-20 x $$

Factor each trinomial completely. See Examples 1 through 7. \(16 p^{4}-40 p^{3}+25 p^{2}\)

Perform each indicated operation. Write all results in lowest terms. $$ \frac{3}{5}+\frac{4}{9} $$

Factor. $$ x^{3}-y^{6} $$

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

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. $$ a^{2} b^{3}+a b^{2}-30 b $$

Factor each trinomial completely. See Examples 1 through 7. \(9 q^{4}-42 q^{3}+49 q^{2}\)

Perform each indicated operation. Write all results in lowest terms. $$ \frac{2}{3}+\frac{3}{7} $$

Factor. $$ 8 x^{3}+27 y^{3} $$

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

Multiply. $$ (2 x+1)(x+5) $$

Factor each trinomial completely. See Examples 1 through 7. \(-2 x^{2}+9 x+5\)

Perform each indicated operation. Write all results in lowest terms. $$ \frac{7}{10}-\frac{5}{12} $$

Factor. $$ 125 x^{3}+8 y^{3} $$

Factor each four-term polynomial by grouping. If this is not possible, write "not factorable by grouping." $$ 7 x-21+x^{3}-2 x^{2} $$

Multiply. $$ (3 x+2)(x+4) $$

Perform each indicated operation. Write all results in lowest terms. $$ \frac{5}{9}-\frac{5}{12} $$

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

Factor each four-term polynomial by grouping. If this is not possible, write "not factorable by grouping." $$ 4 x^{2}-8 x y-3 x+6 y $$

Multiply. $$ (5 y-4)(3 y-1) $$

Factor each trinomial completely. See Examples 1 through 7. \(-4+52 x-48 x^{2}\)

Perform each indicated operation. Write all results in lowest terms. $$ \frac{4}{5} \cdot \frac{7}{8} $$

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

Factor each four-term polynomial by grouping. If this is not possible, write "not factorable by grouping." $$ 5 x y-15 x-6 y+18 $$

Multiply. $$ (4 z-7)(7 z-1) $$

Factor each trinomial completely. See Examples 1 through 7. \(-5+55 x-50 x^{2}\)