Question

If (x-2k) is a factor of f(x), which of the following must be true?
f(2k)=0
f(-2k)=0
A root of f(x) is x=-2k.
or
A y intercept of f(x) is x=2k?

Answer 1

y=f(x)=(x-2k)

if x=2k , then

f(x)=y=0

option d is correct

Answer 2

Answer: If (x-2k) is a factor of f(x), then f(2k)=0.

If (x-2k) is a factor of f(x), it means that f(x) can be written as the product of (x-2k) and another polynomial, say g(x).

So,

                               f(x) = (x-2k)g(x)

This means that when x = 2k, the value of f(x) is zero, i.e.,

                             f(2k) = (2k-2k)g(2k) = 0 * g(2k) = 0

So, in this case, f(2k) must be equal to zero.

The other statements about f(-2k) or a root or y-intercept are not necessarily true just because (x-2k) is a factor of f(x).

learn more about function here

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