Question

Consider the polynomial functionP(x)=x³-8x²-29x+180.State the zeros of P.

Answer 1

x = 4 , x = 9 , x = -5

Explanation:

Given: P(x)=x³-8x²-29x+180

Find the zeros of the polynomial.

First we factor the polynomial and then set each factor to 0.

P(x)=0

Put x=4 into P(x)

`P(4)=4^3-8\cdot 4^2-29\cdot 4+180`

P(4)=0

Divide the polynomial by x-4

`(x^3-8x^2-29x+180)/ (x-4)=x^2-4x-45`

`(x-4)(x^2-4x-45)=0`

`(x-4)(x-9)(x+5)=0`

Set each factor to 0

x - 4 = 0 | x - 9 = 0 | x + 5 = 0

x = 4 , x = 9 , x = -5

Zeros of the polynomial, P(x), are -5,4 and 9