# Thread: Finding the values of p and q.

1. ## Finding the values of p and q.

The expressions px^4-5x+q and x^4-2x^3-px^2-8 have a common factor x-2. Find the values of p and q.
What would be the best way to answer this question? Do I use simultaneous equations?
I'm just really stuck on this one.

2. ## Use the Factor Theorem

Let $f(x)=px^4-5x+q$ and $g(x)=x^4-2x^3-px^2-8$

By using the information in the question and the factor theorem, $f(2)$ and $g(2)=0$

1) $f(2)=p(2)^4-5(2)+q=0$
2) $g(2)=(2)^4-2(2)^3-p(2)^2-8=0$

Two equations, two unknowns: simplify then solve for p and q.

3. Thank you so much.
That's how I was thinking it had to be done, but I just couldn't work it out.
You are brilliant.