Suppose p(x) is a function such that p(x)+(x5+3x3+9x)=(7x3+24x2+25x+1). Express p(x) as a polynomial with the degrees of the terms in decreasing order.
Solution — click to reveal
Isolating p(x), we have: p(x)=(7x3+24x2+25x+1)−(x5+3x3+9x)=−x5+(7−3)x3+24x2+(25−9)x+1=−x5+4x3+24x2+16x+1.