What polynomial has roots of - 6, 1, and 4?

A) x^3 - 9x^2 - 22x + 24

B) x^3 - x^2 - 26x - 24

C) x^3 + x^2 - 26x + 24

D) x^3 + 9x^2 + 14x - 24

The correct option is C.

Step-by-step explanation:

polynomial has roots of - 6, 1, and 4.

We can write it as:

(x+6) (x-1) (x-4)

Now multiply the terms:

First multiply first and second bracket:

{x (x+6) - 1 (x+6) } (x-4)

{ (x^2+6x-x-6) } (x-4)

Solve the like terms:

{ (x^2+5x-6) } (x-4)

x (x^2+5x-6) - 4 (x^2+5x-6)

x^3+5x^2-6x-4x^2-20x+24

Solve the like terms:

x^3+x^2-26x+24

Hence it is proved that the correct option is C ...