Question

Question Show that the binomial is a factor of the polynomial. Then factor the polynomial completely. f(x)=x4−6x3−8x+48; x−6

Answer 1

(x-2)(x²+2x+4)(x-6)

Explanation:

6 | 1 -6 0 -8 48

_____6_0_0_-48__

1 0 0 -8 | 0

As we can see, our remainder is 0, so x-6 is indeed a factor of the polynomial. Also, we can see that the factored polynomial is
`x^4-6x^3-8x+48=(x^3-8)(x-6)=(x-2)(x^2+2x+4)(x-6)`