Question

Determine if x - 2 is a factor of p(x) = x^4 - 3x^2 + 2x - 8, and explain why.

Answer 1

It is a factor of the following equation because it equals zero

Answer 2

Answer:

(x-2) is a factor of the given p(x).

Step-by-step explanation:

A general polynomial

$p(x)=x^n+a_{n-1}x^{n-1}+...+a_{1}x+a_{0}$

can be written as a product of factors

$p(x)=(x-r_{1})(x-r_{2})...(x-r_{n})$

where

$r=1,2,...,n$

are roots of that polynomial.

In the case given in this problem, we have the polynomial

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

and if we evaluate

$p(2)=2^4-3*2^2+2*2-8=16-12+4-8=0$

we confirm that 2 is a root of this polynomial. Therefore, as it could be expressed as a factor of binomials with its roots, we can ensure that (x-2) is a factor of p(x).