Chapter 3

Factor each trinomial and assume that all variables that appear as exponents represent positive integers. $$x^{2 a}+10 x^{a}+21$$

Your classmate solves the equation \(3 a x+b x=0\) for \(x\) as follows: $$ \begin{aligned} 3 a x+b x &=0 \\ 3 a x &=-b x \\ x &=\frac{-b x}{3 a} \end{aligned} $$ How should he know that the solution is incorrect? How would you help him obtain the correct solution?

Factor each trinomial and assume that all variables that appear as exponents represent positive integers. $$6 x^{2 a}-7 x^{a}+2$$

Factor each trinomial and assume that all variables that appear as exponents represent positive integers. $$4 x^{2 a}+20 x^{a}+25$$

Factor each trinomial and assume that all variables that appear as exponents represent positive integers. $$12 x^{2 n}+7 x^{n}-12$$

Factor each trinomial and assume that all variables that appear as exponents represent positive integers. $$20 x^{2 n}+21 x^{n}-5$$

Use this approach to factor Problems \(104-109\). $$(x-3)^{2}+10(x-3)+24$$

Use this approach to factor Problems \(104-109\). $$(3 x-2)^{2}-5(3 x-2)-36$$