MHB ACT Problem: Determine Constant In Polynomial Given Factor

[816318]

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?

 

[MarkFL]

Re: ACT problem

Let:

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

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

$$f(4)=0$$

So, this allows us to write:

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

Can you proceed?

 

[816318]

Re: ACT problem

Let:

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

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

$$f(4)=0$$

So, this allows us to write:

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

Can you proceed?

32-16-z+=0; 16-z=0; 16=z