One factor of x^3 + 4x² - 11x - 30 is x + 2 What are the other factors?

Question

a x - 5 , x + 6

b x - 3, x + 5

c x -6, x + 5

Answer 1

Do the division

. . . . . x^2 + 2x - 15

. . . . . - - - - -- - - - - - - - - - -

x + 2 ) x^3 + 4x^2 - 11x - 30

. . . . . x^3 + 2x^2

. . . . . - - - - - - - -

. . . . . . . . + 2x^2 - 11x

. . . . . . . . + 2x^2 + 4x

. . . . . . . . - - - - - - - - -

. . . . . . . . . . . . . . - 15x - 30

. . . . . . . . . . . . . . - 15x - 30

. . . . . . . . . . . . . . . - - - - - - -

x^2 + 2x - 15

Factors of -15 that add to +2 are +5 & -3

(x + 5)(x - 3) are the other factors

Answer 2

Use synthetic division with -2 outside the bar.

Which yields

1, 2, -15, 0 along the bottom.

Which means the other factor is

x^2 + 2x - 15

By trial factors or other means obtain the factors of that trinomial yielding

x-3, x+5

Answer 3

x^3 + 4x² - 11x - 30

Write out the factors:

(x + 2)(x^2 + bx - 15) ... x^2 because of x^3, -15 because of -30

4x^2 = bx^2 + 2x^2 so b = 2

-11x = -15x + 2bx = -15x + 4x = -11x so b = 2 works here too

(x + 2)(x^2 + 2x - 15)

IN the possible answers only one has 5 and -3 so that is the answer.

(x + 2)(x + 5)(x - 3) is the answer