Brainliest answer goes to whoever answers in the next five determine if x - 2 is a factor of p(x) = x 4 - 3x 2 + 2x - 8, and explain why: )

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Brainliest answer goes to whoever answers in the next five determine if x - 2 is a factor of p(x) = x 4 - 3x 2 + 2x - 8, and explain why: )

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.

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

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

Step-by-step explanation:

A general polynomial

[tex]p(x)=x^n+a_{n-1}x^{n-1}+...+a_{1}x+a_{0}[/tex]

can be written as a product of factors

[tex]p(x)=(x-r_{1})(x-r_{2})...(x-r_{n})[/tex]

where

[tex]r=1,2,...,n[/tex]

are roots of that polynomial.

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

[tex]p(x)=x^4-3x^2+2x-8[/tex]

and if we evaluate

[tex]p(2)=2^4-3*2^2+2*2-8=16-12+4-8=0[/tex]

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).

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).