If f(x)=-4x^3 +5x^2 +8 and c=-2 is c a factor of x?(Use the Factor Theorem)
I think you mis-stated the problem.
Better go back and see just what the theorem says.
It says, Use the Factor theorem to determine whether x-c is a factor of x:
f(x)=-4x^3 +5x^2 +8 and c=-2
That is what it says in the textbook
No, what it says is (x-c) is a factor of f(x).
If (x-c) is a factor of f(x), then f(c) = 0
f(-2) = -4(-8)+5(4)+8 = 32+20+8 ≠ 0
So, (x+2) is not a factor of f(x).
You can check this out at calc101.com by clicking on the "long division" button and entering your polynomials.
To determine if c is a factor of x in the polynomial f(x), we can apply the Factor Theorem, which states that if c is a factor of f(x), then f(c) = 0.
In this case, we need to find out if c = -2 is a factor of f(x) = -4x^3 + 5x^2 + 8. To do that, we substitute c = -2 into the polynomial expression:
f(c) = -4(-2)^3 + 5(-2)^2 + 8
Simplifying the expression:
f(c) = -4(-8) + 5(4) + 8
= 32 + 20 + 8
= 60
Since f(c) = 60 ≠ 0, we can conclude that c = -2 is NOT a factor of x in the polynomial f(x).