Identify the simplest polynomial function that has the given zeros. −2, 4, 5

Question

a. P(x) = x³ − 7x² + 2x − 40

b. P(x) = x³ + 7x² − 2x − 40

c. P(x) = x³ − 7x² + 2x + 40

d. P(x) = x³ + 7x² − 2x + 40

Answer 1

c) is correct

x^3 -7x^2+2x +40

multiply the constants of the factors (each factor has opposite sign of the zero)

(x+2)(x-4)(x-5) 2(-4)(-5) = 40, that eliminates all but c) and d)

(x+2)(x-4)(x-5) = (x^2-2x-8)(x-5) by using FOIL on the 1st two factors

then (-8)(-5) = +40, eliminating a) and b), leaving only c) and d)

-5 times -2x = 10x, x times -8 = -8x. 10x-8x = 2x which c) has but d) doesn't.