Question

What is the remainder R when the polynomial p(x) is divided by (x + 1)? Is (x + 1) a factor of p(x)? p(x) = -3x4 + 2x3 - x2 + 6

Answer 1

Answer:

(x+1) is a factor with remainder 0.

Step-by-step explanation:

We divide (x+1) into the polynomial $-3x^4+2x^3-x^2+6$ through long division or synthetic. We choose long division and look for what will multiply with (x+1) to make the polynomial $-3x^4+2x^3-x^2+6$ .

$(x+1)(-3x^3)=-3x^4-3x^3$

We subtract this from the original $-3x^4-(-3x^4)+2x^3-(-3x^3)-x^2+6$.

This leaves $5x^3-x^2+6$. We repeat the step above.

$(x+1)(5x^2)=5x^3+5x^2$.

We subtract this from $5x^3-(5x^3)-x^2-(5x^2)+6=-6x^2+6$. We repeat the step above.

$(x+1)(-6x)=-6x^2-6x$.

We subtract this from $-6x^2-(-6x^2)+0x-(-6x)+6=6x+6$. We repeat the step above.

$(x+1)(6)=-6x+1$.

We subtract this from $6x-(6x)+6-(6)=0$. There is no remainder. This means (x+1) is a factor.