   Chapter 4.5, Problem 41PS

Chapter
Section
Textbook Problem

For Problems 11-52, perform the indicated divisions. (Objective 1) ( 4 x 3 − 13 x 2 + 8 x − 15 ) ÷ ( 4 x 2 − x + 5 )

To determine

To Find:

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

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 (4x313x2+8x15)÷(4x2x+5).

The following steps are used to solve the problem.

First multiply the divisor by x and write the product 4x3x2+5x under the dividend and subtract.

The value obtained is equals to 12x2+3x.

Now multiply the divisor by 3 and write the product 12x2+3x15 under the dividend simplify.

By using the long division it is written as follows,

4x2x+5x34x313x2+8x15                  4x3x2+5x                  _                           12x2+3x15                             12x2+3x15           _                        �

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