91Ó°ÊÓ

Use a vertical format to find each product. $$\begin{array}{r} 3 y^{3}+2 y^{2}+y+4\\\ \quad \quad y+3\\\ \hline \end{array}$$

Find each product. As we said in the Section 5.3 opener, cut to the chase in each part of the polynomial multiplication: Use only the special-product formula for the sum and difference of two terms or the formulas for the square of a binomial. \((a b-4)^{2}(a b+4)^{2}\) (Do not begin by squaring a binomial.)

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. If \(4 x^{2}+25 x-3\) is divided by \(4 x+1,\) the remainder is 9.

Divide the sum of \((y+4)^{2}\) and \((y+4)(y-4)\) by \(2 y\)

In Exercises \(79-90\), write each number in decimal notation without the use of exponents. $$9.115 \times 10^{9}$$

Find each product. As we said in the Section 5.3 opener, cut to the chase in each part of the polynomial multiplication: Use only the special-product formula for the sum and difference of two terms or the formulas for the square of a binomial. $$[x+y+z][x-(y+z)]$$

use a vertical format to subtract the polynomials. $$\begin{aligned} 7 x^{4}-3 x^{3}+2 x^{2} & \\ -\left(\quad-x^{3}-x^{2}+x-2\right) & \\ -& 1 \end{aligned}$$

The variable \(n\) in each exponent represents a natural number. Divide the polynomial by the monomial. Then use polynomial multiplication to check the quotient. $$\frac{12 x^{15 n}-24 x^{12 n}+8 x^{3 n}}{4 x^{3 n}}$$

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. If polynomial division results in a remainder of zero, then the product of the divisor and the quotient is the dividend.

In Exercises \(79-90\), write each number in decimal notation without the use of exponents. $$7.9 \times 10^{-1}$$