Question

9. (04.03 LC)

Given a polynomial f(x), if (x - 2) is a factor, what else must be true?

f(0) = -2

f(-2) = 0

f(2) = 0

f(0) = 2

show work pls

Answer 1

f(2)=0. The third option is correct.

Explanation:

Suppose we have a polynomial called f(x) and we know (x-2) is a factor of f. This means that we can express f(x) as:

f(x)=(x-2)\cdot g(x)

Being g(x) another unknown function.

Option 1: f(0)=(0-2)\cdot g(0)=-2\cdot g(0). Since we don't know the value of g(0), we cannot assure f(0)=-2. Incorrect

Option 2: f(-2)=(-2-2)\cdot g(-2)=-4\cdot g(-2). Since we don't know the value of g(-2), we cannot assure f(-2)=0. Incorrect

Option 3: f(2)=(2-2)\cdot g(2)=0\cdot g(0)=0. Regardless of the value of g(0), f(0) must be 0. Correct

Option 4: f(0)=(0-2)\cdot g(0)=-2\cdot g(0). Since we don't know the value of g(0), we cannot assure f(0)=2. Incorrect