Write the simplest polynomial function for each set of zeros

Zeros = 0, 1, -1, 5

f(x) = x^4 - 5x^3 - x^2 + 5x should be the answer

Step-by-step explanation:

x = 0 1 -1 5

x = 0

x - 1 = 0

x + 1 = 0

x - 5 = 0

f(x) = x (x - 1) (x + 1) (x - 5)

(x - 1) (x - 5) = x(x) - 1(x) - 5(x) - 1(- 5)

x^2 - x - 5x + 5

f(x) = (x^2 - 6x + 5) (x + 1)

x^2(x) - 6x(x) + 5(x) + x^2(1) - 6x(1) + 5(1)

x^3 - 6x^2 + 5x + x^2 - 6x + 5

f(x) = (x^3 - 5x^2 - x + 5) x

x^3(x) - 5x^2(x) - x(x) + 5(x)

f(x) = (x^4 - 5x^3 - x^2 + 5x)

. + λrh() e 1 1 2 4 4 4 4 4 3 4 4 4 4 4 + th−1(− s(x)2 dx ω + λrh−1() e 2 1 2 4 4

step-by-step explanation: