Is (x + 5) a factor of f(x) = x^3 – 4x^2 + 3x + 7? use either the remainder theorem or the factor theorem to explain your reasoning.

ANSWER

Not a factor

EXPLANATION

The given polynomial has equation:

According to the remainder theorem, if (x+5) is a remainder, then f(-5)=0.

Let us substitute x=-5 into the function and evaluate to see if it will simplify to zero.

Since the remainder is not zero, x+5 is not a factor of

(x+5) is NOT a factor of given function f(x).

Step-by-step explanation:

Given function is .

Now we need to determine if (x+5) is a factor of given function f(x) or not using either the remainder theorem or the factor theorem.

I'm going to use factor theorem which says that "If (x-c) is a factor of f(x) then f(c)=0"

so for (x+5) we have c=-5

Now we need to check if f(-5)=0 or not

which is not equal to 0.

Hence (x+5) is NOT a factor of given function f(x).

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f(x) is going down by 4

step-by-step explanation:

(its either that or its going left by 4)