91影视

In Exercises \(53-78,\) divide the polynomial by the monomial. Check each answer by showing that the product of the divisor and the quotient is the dividend. $$\frac{20 x^{4}+5 x^{3}}{5}$$

Simplify each exponential expression. Assume that variables represent nonzero real numbers. $$\left(\frac{x^{6}}{x^{2}}\right)^{-3}$$

Determine whether each statement 鈥渕akes sense鈥� or 鈥渄oes not make sense鈥� and explain your reasoning. Each statement applies to the division problem. $$\frac{x^{3}+1}{x+1}$$ Rewriting \(x^{3}+1\) as \(x^{3}+0 x^{2}+0 x+1\) can change the value of the variable expression for certain values of \(x .\)

Determine whether each statement 鈥渕akes sense鈥� or 鈥渄oes not make sense鈥� and explain your reasoning. Each statement applies to the division problem. $$\frac{x^{3}+1}{x+1}$$ There's no need to apply the long-division process to this problem because I can work the problem in my head and see that the quotient must be \(x^{2}+1\).

Find each product. $$(a b+1)(a b-1)$$

Subtract the polynomials. $$(x-8)-(3 x+2)$$

In Exercises \(53-78,\) divide the polynomial by the monomial. Check each answer by showing that the product of the divisor and the quotient is the dividend. $$\frac{14 x^{4}-7 x^{3}}{7 x}$$

In Exercises \(45-62,\) multiply using the rules for the square of a binomial. $$(7-2 x)^{2}$$

Find each product. In each case, neither factor is a monomial. $$(x+3)(x+5)$$

Simplify each exponential expression. Assume that variables represent nonzero real numbers. $$\left(\frac{4 x^{5}}{2 x^{2}}\right)^{-4}$$