Question

Which of the following is a factor of:

f(x)=x5−2x4+3x3−6x2−4x+8

Select the appropriate response:

A) (5x − 27)
B) (6x − 2)
C) ( x − 9)
D) (x − 2)

Answer 1

D) (x-2)

Explanation:

Let's try each factor out with synthetic division:

Option D: x^5-2x^4+3x^3-6x^2-4x+8 / x-2 = 2 | 1 -2 3 -6 -4 8 = x^4+3x^2-4 with no remainder so D works

Option C: x^5-2x^4+3x^3-6x^2-4x+8 / x-9 = 9 | 1 -2 3 -6 -4 8 = x^4+7x^3+66x^2+588x+5288 with a remainder of 47600 so C can't work

Option B: Doesn't work

Option A: Doesn't work

Therefore, D is the right answer because there's no remainder.

Hope this made sense, I tried.

Answer 2

Hello the answer is D -2

Explanation:

^5-2x ^4+3x ^3-6x^2-4+8 / x-2 = 2 | 1 -2 3 -6 -4 8 = ^4+3 ^2-