Find the polynomial and use the factored form to find the ze

Find the polynomial and use the factored form to find the zeros. (Enter your answer as a comma-separated list. Enter all answers including repetitions.) P(X) = 2x^3 + x^2 - 8x + 4

Solution

P(x)=2x³-x²-8x+4

P(x)=(2x-1)(x+2)(x-2)

for zeroes (2x-1)(x+2)(x-2)=0

(2x-1)=0,(x+2)=0,(x-2)=0

x= 1/2 , -2 ,2

or

by rational root test possible solutions are -1,1,-1/2, 1/2,-2,2,-4,4

P(-1)=-2-1+8+4 =9

P(1)=2-1-8+4 =-3

P(-1/2)=15/2

P(1/2)=0

P(-2)=0

P(2)=0

P(-4)=-108

P(4)=84

P(x)=0 for x= 1/2 , -2 ,2