Kade Reese

Answered

2022-07-19

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

Answer & Explanation

Shelby Strong

Expert

2022-07-20Added 9 answers

We will divide by long division method and write the function in required form.
$p\left(x\right)=-3{x}^{2}-2{x}^{2}+2x-1\phantom{\rule{0ex}{0ex}}{x}^{2}+4x+4\sqrt{-3{x}^{3}-2{x}^{2}+2x-1}-3x+10\phantom{\rule{0ex}{0ex}}-3{x}^{3}-12{x}^{2}-12x\phantom{\rule{0ex}{0ex}}10{x}^{2}+14x-1\phantom{\rule{0ex}{0ex}}10{x}^{2}+40x+40\phantom{\rule{0ex}{0ex}}-24x-41$
Here divisor $\left(d\left(x\right)\right)={x}^{2}+4x+4$
quotient $\left(q\left(x\right)\right)=-3x+10$
remainder $r\left(x\right)=-24x-41$
Therefore p(x) is
$p\left(x\right)=\left({x}^{2}+4x+4\right)\left(-3x+10\right)+\left(-24x-41\right)$

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