Question

Which of the following is a factor of x4 + 3x3 - 5x2 + 2x – 24?

A.) x – 2
B.) x – 3
C.) x – 5
D.) Not factorable

Answer 1

Note: This is not middle school math. If it is, god your screwed.

Answer:

A) x-2

Explanation:

To find a factor of an equation, you must divide the equation by a binomial (which is the answer choices). Also, when you divide, it is only declared factorable when there is NO REMAINDER. Not even if it's 1 remainder.

Answer 2

A) x-2

EXPLANATION

Using the Remainder Theorem, if x=a is a factor of p(x), then p(a)=0.

Let

`p(x) = {x}^(4) + 3 {x}^(3) - 5 {x}^(2) + 2x - 24`

`p(2) = {2}^(4) + 3 {(2)}^(3) - 5 {(2)}^(2) + 2(2) - 24`

`p(2) = 16+ 24 - 20 + 4- 24`

`p(2) = 24- 24 = 0`

Since

`p(2) =0`

x-2 is a factor of

`p(x) = {x}^(4) + 3 {x}^(3) - 5 {x}^(2) + 2x - 24`

For the other options,

`p(3) =99`

`p(5) =861`

Hence x-3 and x-5 are not factors of the given function.

The correct answer is A.