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.
Thanks in advance everyone.
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.
Thanks in advance everyone.
Let $\displaystyle f(x)=px^4-5x+q$ and $\displaystyle g(x)=x^4-2x^3-px^2-8$
By using the information in the question and the factor theorem, $\displaystyle f(2)$ and $\displaystyle g(2)=0$
1) $\displaystyle f(2)=p(2)^4-5(2)+q=0$
2) $\displaystyle g(2)=(2)^4-2(2)^3-p(2)^2-8=0$
Two equations, two unknowns: simplify then solve for p and q.