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

Question

zepdrix · Answer

What else must be true?
Hmm lots of stuff... this question is strangely broad.

x=2 is a zero of the function.
f(x)/(x-2) is a polynomial.

zepdrix · Answer

Do you have some multiple choice options? :)

anonymous · Answer

f(0) = 2
 f(0) = −2
 f(−2) = 0
 f(2) = 0

anonymous · Answer

I was thinking the first one

zepdrix · Answer

So like I mentioned, x=2 is a zero of the function.
That means when you replace x with 2, the function output is zero.

A? I think you've got that backwards.
In A, they've replaced x with 0 and the output is 2.
f(x) -> f(0)

anonymous · Answer

Oh okay, my bad. So it's the last one. You substitute x for 0

zepdrix · Answer

You substitute 2 for x...
yes the last one :P

anonymous · Answer

Ugh yeah, that's I meant lol. I was still thinking of A. Thank you so much :)

anonymous · Answer

Do you mind helping me with another one?

anonymous · Answer

Which polynomial identity will prove that 49 = (2 + 5)2?
Difference of Squares
 Difference of Cubes
 Sum of Cubes
 Square of a Binomial

I think it's difference of squares

zepdrix · Answer

Recall that in math, the word `difference` means `subtraction`.
So that refers to some formula involving subtraction.

No subtraction in our problem though, ya?

anonymous · Answer

Oh yeah. So it can't be A or B and this problem isn't a binomial so it's C?

zepdrix · Answer

Well are you familiar with these words they're using?
What is a cube? how large?
How large is a square?

anonymous · Answer

A cube is like a 3d square, it can be any size but all sides need to be the same.

anonymous · Answer

Wait... if it's (2+5)^2 and you were to write it out; (2+5) * (2+5) that would be a binomial.

zepdrix · Answer

3d is the key there.
So in multiplication it's something being multiplied by itself 3 times.
But we don't have that in our problem, ya?
(2+5)^2 =/= (2+5)(2+5)(2+5)
We don't have a cube.

zepdrix · Answer

So square ya :)
and yes a binomial is just two things being added or subtracted

anonymous · Answer

I knew it wasn't a cube because it was being squared, not cubed. Thank you again! :)

anonymous · Answer

Can you help me with this last one? This one I don't really know how to solve.

anonymous · Answer

Using a directrix of y = 5 and a focus of (4, 1), what quadratic function is created?

anonymous · Answer

Answer choices: 
 f(x) = one fourth (x − 4)2 − 3
 f(x) = one eighth (x + 4)2 − 3
 f(x) = −one eighth (x − 4)2 + 3
 f(x) = −one fourth (x + 4)2 − 3