Find a polynomial f(x) of degree 3 that has the following zeros: 0,4,-1. Leave your answer in factored form.

Answer 1

x(x-4)(x+1) is a 3 degree polynomial in factored form with zeros 0,4 and -1

Just take each zero and change its sign, then stick an x in front of it to get the 3 factors

(x-0)(x-4)(x- -1) = x(x-4)(x+1)

= x(x^2-3x-4)

= f(x) = x^3 -3x^2 -4x

f(0) = 0

f(4) = 64-3(16)-4(4) = 0

f(-1) = -1 -3(-1)^2 -4(-1) = 0

graph the polynomial and it intersects the x axis in 3 places, the origin (0,0), (4,0) and (-1,0)