   Chapter 4.5, Problem 43PS

Chapter
Section
Textbook Problem

For Problems 11-52, perform the indicated divisions. (Objective 1) ( 5 a 3 + 7 a 2 − 2 a − 9 ) ÷ ( a 2 + 3 a − 4 )

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 using the long-division method.

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.

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

The product obtained is subtracted from the dividend.

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

Calculation:

Consider the expression (5a3+7a22a9)÷(a2+3a4).

The following steps are used to solve the division problem.

First multiply the divisor by 5a and write the product  5a3+15a220a under the dividend and subtract.

The value obtained is equals to 8a2+18a.

Now multiply the divisor by 8 and write the product 8a224a+32 under the dividend and simplify.

By using the long division it is written as follows,

a2+3a45a85a3+7a22a9                   5a3+15a220a       _                         8a2+18a9                              8a224a+32      _                                         42a41

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