   Chapter 4.5, Problem 45PS

Chapter
Section
Textbook Problem

For Problems 11-52, perform the indicated divisions. (Objective 1) ( 2 n 4 + 3 n 3 − 2 n 2 + 3 n − 4 ) ÷ ( n 2 + 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 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 (2n4+3n32n2+3n4)÷(n2+1).

The following steps are used to solve the division problem.

First multiply the divisor by  2n2 and write the product 2n4+2n2  under the dividend and subtract.

The value obtained is equals to 3n34n2.

Now multiply the divisor by 3n and write the product  3n3+3n under the dividend and

subtract.

The value obtained is equals to 4n2.

Multiply the divisor by 4 and write the product 4n24 under the dividend and simplify.

By using the long division it is written as follows,

n2+12n2+3n42n4+3n32n2+3n4          2n4 +0n3+2n2             _                    3n34n2+3n                       3n30n2+3n      _                            4n24                              4n24      �

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