Question

Find the remainder of -2x^4-6x^2+3x+1 divide x+1
Explain how each theorem can be used in determining the solutions for a polynomial equation. Descartes Rule of Signs and Rational Root Theorem

Answer 1

( -2x^4-6x^2+3x+1)/(x+1) = (-2x^3+2x^2-8x+11) - 10/(x+1)

Answer 2

you can find the remainder by replacing \(x\) by -1 and computing

Answer 3

because if \[\frac{-2x^4-6x^2+3x+1}{x+1}=q(x)+\frac{r}{x+1}\] that means
\[-2x^4-6x^2+3x+1=(x+1)q(x)+r\] and so replacing x by -1 gives
\[-2(-1)^3-6(-1)^2+3(-1)+1=(-1+1)q(-1)+r=0+r=r\]