# Thread: ACT Problem: Determine Constant In Polynomial Given Factor

1. Assume that (x-4) is a factor of 2x^2-4x-z. What is the value of z?

How would you set it up to use the foil method?

2. Let:

$\displaystyle f(x)=2x^2-4x-z$

Now, if $x-4$ is a factor of $f$, then we must have:

$\displaystyle f(4)=0$

So, this allows us to write:

$\displaystyle 2(4)^2-4(4)-z=0$

Can you proceed?

Originally Posted by MarkFL
Let:

$\displaystyle f(x)=2x^2-4x-z$

Now, if $x-4$ is a factor of $f$, then we must have:

$\displaystyle f(4)=0$

So, this allows us to write:

$\displaystyle 2(4)^2-4(4)-z=0$

Can you proceed?
32-16-z+=0; 16-z=0; 16=z