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:
[tex]( 2x^{4}+7x^{3}-18x^{2}+11x-2 )/ 2x^{2}-3x+1[/tex]
Steps to follow:
Divide the leading term of the dividend by the leading term of the divisor: 2[tex]x^{4}[/tex]/2x²=x².
Multiply it by the divisor: x²(2x²−3x+1)=2[tex]x^{4}[/tex]−3x³+x².
Subtract the dividend from the obtained result:
[tex]( 2x^{4}+7x^{3}-18x^{2}+11x-2 )[/tex]- ( [tex]x^{4}[/tex]−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:
https://brainly.com/question/14780388
#SPJ1
