A mysterious box is delivered to the dinner party you are attending. The label on the box says that the volume of a box is the function f (x) = x3 + 3x2 - 10x - 24. To open the box, you need to identify the correct factors of f (x). Partygoers offer up solutions, and it is your job to find the right ones.

Their suggestions are:

• (x - 1)

• (x + 2)

• (x - 3)

• (x + 4)

• (x + 6)

• (x - 12)

List the correct factors. Then justify your selections with complete sentences.

Question

Mathematics

Nicolas Medina

28 May, 03:10

A mysterious box is delivered to the dinner party you are attending. The label on the box says that the volume of a box is the function f (x) = x3 + 3x2 - 10x - 24. To open the box, you need to identify the correct factors of f (x). Partygoers offer up solutions, and it is your job to find the right ones.

Their suggestions are:

• (x - 1)

• (x + 2)

• (x - 3)

• (x + 4)

• (x + 6)

• (x - 12)

List the correct factors. Then justify your selections with complete sentences.

+5

Answers (1)

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Golden · Answer 1

F (x) = x³ + 3x² - 10x - 24

The root factors must be the factors of 24.

1 x 24; 2 x 12; 3 x 8; 4 x 6.

The most probable roots would be - 4, - 3, - 2, - 1, 1, 2, 3, or 4.

Using synthetic division, one can find that the smallest root is - 3.

(x - 3) (x² - 6x - 8). The quadratic can now be factored as (x + 2) (x - 4) and further factored as (x - 3) (x + 2) (x - 4).

The correct factors are: (x - 3) (x + 2) (x - 4)