Kade Reese

Answered

2022-07-19

Consider the polynomial function $p(x)=-3{x}^{3}-2{x}^{2}+2x-1$

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.

$\frac{-3{x}^{3}-2{x}^{2}+2x-1}{{x}^{2}+4x+4}$

p(x)=

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.

$\frac{-3{x}^{3}-2{x}^{2}+2x-1}{{x}^{2}+4x+4}$

p(x)=

Answer & Explanation

Shelby Strong

Expert

2022-07-20Added 9 answers

We will divide by long division method and write the function in required form.

$p(x)=-3{x}^{2}-2{x}^{2}+2x-1\phantom{\rule{0ex}{0ex}}{x}^{2}+4x+4\sqrt{-3{x}^{3}-2{x}^{2}+2x-1}-3x+10\phantom{\rule{0ex}{0ex}}-3{x}^{3}-12{x}^{2}-12x\phantom{\rule{0ex}{0ex}}10{x}^{2}+14x-1\phantom{\rule{0ex}{0ex}}10{x}^{2}+40x+40\phantom{\rule{0ex}{0ex}}-24x-41$

Here divisor $(d(x))={x}^{2}+4x+4$

quotient $(q(x))=-3x+10$

remainder $r(x)=-24x-41$

Therefore p(x) is

$p(x)=({x}^{2}+4x+4)(-3x+10)+(-24x-41)$

$p(x)=-3{x}^{2}-2{x}^{2}+2x-1\phantom{\rule{0ex}{0ex}}{x}^{2}+4x+4\sqrt{-3{x}^{3}-2{x}^{2}+2x-1}-3x+10\phantom{\rule{0ex}{0ex}}-3{x}^{3}-12{x}^{2}-12x\phantom{\rule{0ex}{0ex}}10{x}^{2}+14x-1\phantom{\rule{0ex}{0ex}}10{x}^{2}+40x+40\phantom{\rule{0ex}{0ex}}-24x-41$

Here divisor $(d(x))={x}^{2}+4x+4$

quotient $(q(x))=-3x+10$

remainder $r(x)=-24x-41$

Therefore p(x) is

$p(x)=({x}^{2}+4x+4)(-3x+10)+(-24x-41)$

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