Find the zeros of the polynomial function Enter your answers

Find the zeros of the polynomial function. (Enter your answers as a comma-separated list. Enter all answers including repetitions.) P(x) - x^5 + 10x^4 + 40x^3 + 80x^2 + 80x + 32

Solution

p(x) = x^5 + 10x^4 + 40x^3 + 80 x^2 + 80 x + 32

setting the polynomial to 0 to find the zeros of the function

rational zeros of the function are

+- { 1,2,4,8,16,32} / 1

by checking each rational zero one by one

we find that actual zero is at x = -2 , plug x = -2 in teh eqiuation

x^5 + 10x^4 + 40x^3 + 80 x^2 + 80 x + 32 = (-2)^5 +10(-2)^4 + 40(-2)^3 + 80(-2)^2 + 80(-2) + 32

hence it comes out to be 0

therefore , zero is x = -2