91Ó°ÊÓ

For Problems \(105-110\), factor each expression. Assume that all variables that appear as exponents represent positive integers. $$ 6 x^{3 a}-10 x^{2 a} $$

Consider the following approach to factoring the problem $$\begin{aligned} &(x-2)^{2}+3(x-2)-10 \\ &(x-2)^{2}+3(x-2)-10 \\ &=y^{2}+3 y-10 \\ &=(y+5)(y-2) \\ &=(x-2+5)(x-2-2) \\ &=(x+3)(x-4) \end{aligned}$$ Use this approach to factor Problems \(110-115\). $$ (x-3)^{2}+10(x-3)+24 $$

Consider the following approach to factoring the problem $$\begin{aligned} &(x-2)^{2}+3(x-2)-10 \\ &(x-2)^{2}+3(x-2)-10 \\ &=y^{2}+3 y-10 \\ &=(y+5)(y-2) \\ &=(x-2+5)(x-2-2) \\ &=(x+3)(x-4) \end{aligned}$$ Use this approach to factor Problems \(110-115\). $$ (x+1)^{2}-8(x+1)+15 $$

Consider the following approach to factoring the problem $$\begin{aligned} &(x-2)^{2}+3(x-2)-10 \\ &(x-2)^{2}+3(x-2)-10 \\ &=y^{2}+3 y-10 \\ &=(y+5)(y-2) \\ &=(x-2+5)(x-2-2) \\ &=(x+3)(x-4) \end{aligned}$$ Use this approach to factor Problems \(110-115\). $$ (3 x-2)^{2}-5(3 x-2)-36 $$

Consider the following approach to factoring the problem $$\begin{aligned} &(x-2)^{2}+3(x-2)-10 \\ &(x-2)^{2}+3(x-2)-10 \\ &=y^{2}+3 y-10 \\ &=(y+5)(y-2) \\ &=(x-2+5)(x-2-2) \\ &=(x+3)(x-4) \end{aligned}$$ Use this approach to factor Problems \(110-115\). $$ 6(x-4)^{2}+7(x-4)-3 $$

Consider the following approach to factoring the problem $$\begin{aligned} &(x-2)^{2}+3(x-2)-10 \\ &(x-2)^{2}+3(x-2)-10 \\ &=y^{2}+3 y-10 \\ &=(y+5)(y-2) \\ &=(x-2+5)(x-2-2) \\ &=(x+3)(x-4) \end{aligned}$$ Use this approach to factor Problems \(110-115\). $$ 15(x+2)^{2}-13(x+2)+2 $$