Question

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

x3 − 9x2 − 22x + 24
x3 − x2 − 26x − 24
x3 + x2 − 26x + 24
x3 + 9x2 + 14x − 24

Answer 1

Answer:

x^3+9x^2+14x-24 has roots of -6,-4 and 1

Option D is correct

Step-by-step explanation:

If the polynomial has roots of -6 -4 and 1

then x=-6, x=-4, x=1

Which can be written as:

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

Multiplying we get,

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

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

(x+6)(x^2+3x-4)

x(x^2+3x-4)+6(x^2+3x-4)

x^3+3x^2-4x+6x^2+18x-24

x^3+3x^2+6x^2-4x+18x-24

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

So, x^3+9x^2+14x-24 has roots of -6,-4 and 1

Option D is correct

Answer 2

(x+6)(x+4)(x-1) should be the polynomial in factored form. (see how I came up with that from the roots?)
Expand this, and see which answer choice matches it
(x-1)(x^2 - 10x + 24)
Expanding it the rest of the way and determining the answer has been left as an exercise for the reader.