91Ó°ÊÓ

Find the indicated products. Assume all variables that appear as exponents represent positive integers. $$\left(2 x^{n}+5\right)^{2}$$

Find the indicated products. Assume all variables that appear as exponents represent positive integers. $$\left(3 x^{n}-7\right)^{2}$$

Find each product. Assume that the variables in the exponents represent positive integers. For example, $$ \left(x^{2 n}\right)\left(x^{3 n}\right)=x^{2 n+3 n}=x^{5 n} $$ $$\left(4 x^{2 n-1}\right)\left(-3 x^{n+1}\right)$$

Should help you pull together all of the factoring techniques of this chapter. Factor completely each polynomial, and indicate any that are not factorable using integers. $$18 x^{2}-12 x+2$$

Solve each equation for the indicated variable. \(3 a y^{2}=b y\) for \(y\)

Solve each equation for the indicated variable. \(y^{2}-a y+2 b y-2 a b=0\) for \(y\)

Should help you pull together all of the factoring techniques of this chapter. Factor completely each polynomial, and indicate any that are not factorable using integers. $$x^{4}-5 x^{2}-36$$

Find each product. Assume that the variables in the exponents represent positive integers. For example, $$ \left(x^{2 n}\right)\left(x^{3 n}\right)=x^{2 n+3 n}=x^{5 n} $$ $$\left(-3 a^{2}\right)\left(-4 a^{n+2}\right)$$

Solve each equation for the indicated variable. \(x^{2}+a x+b x+a b=0\) for \(x\)

Should help you pull together all of the factoring techniques of this chapter. Factor completely each polynomial, and indicate any that are not factorable using integers. $$6 x^{4}-5 x^{2}-21$$