Is (x + 7) a factor of f(x) = x^3 − 3x^2 + 2^x − 8? Use either the remainder theorem or the factor theorem to explain your reasoning.

We can use Factor Theorem to answer this question. According to this theorem, in order to find if (x - a) is a factor of a polynomial f(x), calculate f(a). If f(a) comes out to be equal to zero, this will mean that (x-a) is factor of f(x).

Here, the expression we have is (x + 7), so we need to find f(-7) in order to check if (x+7) is a factor of f(x) or not

[tex]f(x)=x^{3}-3x^{2}+2x-8[/tex]

Substituting x = -7, we get:

[tex]f(-7)=(-7)^{3}-3(-7)^{2}+2(-7)-8\\\\ f(-7)=-512[/tex]

Since f(-7) ≠ 0, (x + 7) is not a factor of the polynomial f(x)

wasantawfeeq wasantawfeeq · Answer 2 · 2020-11-13T01:31:53+01:00

Answer:

is not a factor

Step-by-step explanation:

Step-by-step explanation

We know that,

The factor theorem is a theorem that links the factors and the roots of a polynomial.

The theorem is as follows:

A polynomial f(x) has a factor (x−p) if and only if f(p)=0.

Consider,

f(x)=x

3

−3x

2

+2x−8

& (x+7) =(x−(−7))

Here,

p=−7

Now, lets check:

f(−7)=(−7)

3

−3(−7)

2

+2(−7)−8

f(−7)=(−343)−3(49)−14−8

f(−7)=−343−147−14−8

f(−7)=−512 , which is not equal to 0 .

So, According to the Factor theorem, we got

(x+7) is not a factor of f(x)=x

3

−3x

2

+2x−8.