Question

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

Answer 1

The correct option is C.

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....