Answer:
x = 4 , x = 9 , x = -5
Step-by-step 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)
[tex]P(4)=4^3-8\cdot 4^2-29\cdot 4+180[/tex]
P(4)=0
Divide the polynomial by x-4
[tex](x^3-8x^2-29x+180)\div (x-4)=x^2-4x-45[/tex]
[tex](x-4)(x^2-4x-45)=0[/tex]
[tex](x-4)(x-9)(x+5)=0[/tex]
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
