Answer to Question #324539 in Linear Algebra for Busi

Question

Find a polynomial, P(x), of degree 3 with zeros of 4,1 and −1, if P(0) = 8

Answer 1

$P(x)=a(x-4)(x-1)(x+1)$.

$P(0)=8 \to a(-4)(-1)*1=8 \to a=2.$

$P(x)=2(x-4)(x-1)(x+1)=2x^3-8x^2-2x+8.$