Question

Tamara and clyde got different answers when dividing 2x4 7x3 – 18x2 11x – 2 by 2x2 – 3x 1. analyze their individual work.

Answer 1

The process to divide the polynomial is discussed below:

What is Polynomial Division?

Polynomial long division is an algorithm for dividing a polynomial by another polynomial of the same or lower degree, a generalized version of the familiar arithmetic technique called long division.

Given:

$( 2x^{4}+7x^{3}-18x^{2}+11x-2 )/ 2x^{2}-3x+1$

Steps to follow:

Divide the leading term of the dividend by the leading term of the divisor: 2$x^{4}$/2x²=x².

Multiply it by the divisor: x²(2x²−3x+1)=2$x^{4}$−3x³+x².

Subtract the dividend from the obtained result:

$( 2x^{4}+7x^{3}-18x^{2}+11x-2 )$- ( $x^{4}$−3x³+x². ) =10x³−19x²+11x−2.

Divide the leading term of the obtained remainder by the leading term of the divisor: 10x³/2x²=5x.

Multiply it by the divisor: 5x(2x²−3x+1)=10x³−15x²+5x.

Subtract the remainder from the obtained result: (10x³−19x²+11x−2)−(10x³−15x²+5x)=−4x²+6x−2.

Divide the leading term of the obtained remainder by the leading term of the divisor: −4x²/2x²=−2.

Multiply it by the divisor: −2(2x²−3x+1)=−4x²+6x−2.

Subtract the remainder from the obtained result:

(−4x²+6x−2)−(−4x²+6x−2)=0.

Learn more about long division here:

brainly.com/question/14780388

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