Consider the polynomial function p(x)=−3x^3−2x^2+2x−1. Use polynomial long division to perform the indicated division and rewrite the polynomial in the form p(x)=d(x)q(x)+r(x), where d is the divisor, q is the quotient, and r is the remainder. (−3x^3−2x^2+2x−1)/(x^2+4x+4) p(x)=?

Kade Reese

Kade Reese

Answered question

2022-07-19

Consider the polynomial function p ( x ) = 3 x 3 2 x 2 + 2 x 1
Use polynomial long division to perform the indicated division and rewrite the polynomial in the form p(x)=d(x)q(x)+r(x), where d is the divisor, q is the quotient, and r is the remainder.
3 x 3 2 x 2 + 2 x 1 x 2 + 4 x + 4
p(x)=

Answer & Explanation

Shelby Strong

Shelby Strong

Beginner2022-07-20Added 9 answers

We will divide by long division method and write the function in required form.
p ( x ) = 3 x 2 2 x 2 + 2 x 1 x 2 + 4 x + 4 3 x 3 2 x 2 + 2 x 1 3 x + 10 3 x 3 12 x 2 12 x 10 x 2 + 14 x 1 10 x 2 + 40 x + 40 24 x 41
Here divisor ( d ( x ) ) = x 2 + 4 x + 4
quotient ( q ( x ) ) = 3 x + 10
remainder r ( x ) = 24 x 41
Therefore p(x) is
p ( x ) = ( x 2 + 4 x + 4 ) ( 3 x + 10 ) + ( 24 x 41 )

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