jmc
algebra intermediate
Problem
Let f(x)=x+5 and let g(x)=x2+1. Let p(x)=g(x)+f(x) and let q(x)=g(x)−f(x). Find p(x)⋅q(x).
Solution — click to reveal
We know p(x)=(x2+1)+(x+5)=x2+x+6. Also, q(x)=(x2+1)−(x+5)=x2−x−4. We want to find p(x)⋅q(x), so we substitute:
p(x)⋅q(x)=(x2+x+6)(x2−x−4)=x2(x2−x−4)+x(x2−x−4)+6(x2−x−4)=x4−x3−4x2+x3−x2−4x+6x2−6x−24=x4+(−1+1)x3+(−4−1+6)x2+(−4−6)x−24=x4+x2−10x−24.
Final answer
x^4+x^2-10x-24