Chapter 4.5, Problem 21PS

### Intermediate Algebra

10th Edition
Jerome E. Kaufmann + 1 other
ISBN: 9781285195728

Chapter
Section

### Intermediate Algebra

10th Edition
Jerome E. Kaufmann + 1 other
ISBN: 9781285195728
Textbook Problem

# For Problems 11-52, perform the indicated divisions. (Objective 1) ( 2 x 3 + 9 x 2 − 17 x + 6 ) ÷ ( 2 x − 1 )

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 (2x3+9x2âˆ’17x+6)Ã·(2xâˆ’1).

The following steps are used to solve the problem.

First multiply the divisor by x2 and write the product 2x3âˆ’x2 under the dividend and subtract.

The value obtained is equals to 10x2.

Now multiply the divisor by 5x and write the product 10x2âˆ’5x under the dividend subtract.

The value obtained is equals to âˆ’12x.

Now multiply the divisor by âˆ’6 and write the product âˆ’12x+6Â  under the dividend and simplify.

By using the long division it is written as follows,

2xâˆ’1x2+5xâˆ’62x3+9x2âˆ’17x+6Â Â Â Â Â Â Â Â Â Â Â 2x3âˆ’x2Â Â Â Â Â Â Â Â Â Â Â _Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 10x2âˆ’17xÂ Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 10x2âˆ’5xÂ Â Â Â Â Â Â Â Â Â _Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â âˆ’12x+6Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â âˆ’12x+6Â Â Â Â Â Â Â Â Â Â Â <

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