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Let $P(x)$ be a cubic polynomial such that $P(0) = -3$ and $P(1) = 4.$ When $P(x)$ is divided by $x^2 + x + 1,$ the remainder is $2x - 1.$ What is the quotient when $P(x)$ is divided by $x^2 + x + 1$?

 

Here is my go at it:

Let us make the polynomial:

ax^3+bx^2+cx+d, when 0 is plugged in, this equation gives -3, therefore d=-3

next, P(1)=4 so a*1+b*1+c*1-3=4, therefore, a+b+c=7, what do I do know? I am really confused.

 Dec 30, 2020
 #1
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Using the factor theorem and remainder theorem, I get that the quotient is 3x + 4.

 Dec 31, 2020

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