Chapter 4.5, Problem 66PS

### 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

# Give a step-by-step description of how you would do the following division problem. ( 4 − 3 x − 7 x 3 ) ÷ ( x + 6 )

To determine

To Find:

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

Explanation

Approach:

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

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

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

3. The product obtained is subtracted from the dividend.

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

Calculation:

Consider the expression (4âˆ’3xâˆ’7x3)Ã·(x+6).

The following steps are used to solve the division problem.

First arrange the polynomial in the descending order.

Then the polynomial becomes as follows,

âˆ’7x3âˆ’3x+4

First multiply the divisor by âˆ’7x2 and write the product âˆ’7x3âˆ’42x2 under the dividend and subtract.

The value obtained is equals to 42x2âˆ’3x.

Now multiply the divisor by 42x and write the product 42x2âˆ’252x under the dividend and

Subtract.

The value obtained is equals to 249x+4.

Again multiply the divisor by 249 and write the product 249x+1494 under the dividend and

Simplify.

By using the long division it is written as follows,

Â Â Â Â Â Â Â Â âˆ’7x2+42x+249x+6)âˆ’7x3+0x2âˆ’3x+4Â Â Â Â Â Â Â Â âˆ’7x3âˆ’42x2 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 42x2âˆ’3xÂ 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 42x2âˆ’252xÂ Â Â Â Â Â Â Â Â âˆ’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 Â Â Â Â Â Â Â 249x+4<

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