   Chapter 4.5, Problem 28PS

Chapter
Section
Textbook Problem

For Problems 11-52, perform the indicated divisions. (Objective 1) x 3 + 64 x + 4

To determine

To Find:

The value of the polynomials by performing the indicated division by binomials.

Explanation

Division of a polynomial by binomial is done by long-division method.

In this method to find the first quotient term, divide the first dividend term by the first divisor term.

Multiply the divisor with the term obtained by dividing the first dividend term with the first quotient term.

The product obtained is subtracted from the dividend.

Repeat the same process to divide the other terms of the dividend.

Calculation:

Consider the expression x3+64x+4.

The following steps are used to solve the problem.

First multiply the divisor by  x2 and write the product x3+4x2  under the dividend and subtract.

The value obtained is equals to 4x2.

Now multiply the divisor by 4x2 and write the product under the dividend subtract.

The value obtained is equals to  16x.

Now multiply the divisor by 16 and write the product 16x+64 under the dividend and simplify.

By using the long division it is written as follows,

x+4x24x+16x3+0x2+0x+64         x3+4x2            _              4x2+0x                    4x216x           _                                16x+64                          &#

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