Question

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Determine if x - 2 is a factor of p(x) = x 4 - 3x 2 + 2x - 8, and EXPLAIN WHY:)

Answer 1

If x-2 is a factor of the polynomial, then x = 2 must make it zero.
We proceed to replace x = 2 in the polynomial:
16-12+4-8 = 0
As we can see, x-2 is a factor of the polynomial.
Factoring the expression, we obtain:
(x-2)(x^3+2x^2+x+4)
It is shown that x-2 is a factor of the polynomial.

Answer 2

Answer:

yes.

Step-by-step explanation:

To see if x-2 is a factor of p(x), first thing to do would be to substitute x = 2 into the function:

p(x) = x^4 - 3x^2 + 2x - 8

x = 2,

p(2) = 2^4 - 3(2)^2 + 2(2) - 8

p(2)= 16 - 12 + 4 - 8

p(2)= 0

If p(x) is 0, means that it is the correct factor. If

p(x) is not equals to 0, it is not a factor of p(x). Therefore, x-2 is a factor of p(x).