Question

Which shows one way to determine the factors of x^3+11x^2-3x-33 by grouping?

A. X^2(x+11)+3(x-11)

B. X^2(x-11)-3(x-11)

C. X^2(x+11)+3(x+11)

D. X^2(x+11)-3(x+11)

Answer 1

That would be Option D

The last step would be
= (x^2 - 3)(x + 11)

Answer 2

The correct answer is D.
`x^2\left(x+11\right)-3\left(x+11\right)`.

Explanation:

To factor the expression
`x^3+11x^2-3x-33` by grouping you must:

First, notice that there is no factor common to all terms. However, if we group the first two terms together and the last two terms together, each group has its own greatest common factor.

`\left(x^3+11x^2\right)+\left(-3x-33\right)`

Second, factor out
`x^2` from
`x^3+11x^2`:

`x^2\left(x+11\right)`

Next, factor out
`-3` from
`-3x-33`:

`-3\left(x+11\right)`

Therefore,

`x^3+11x^2-3x-33=x^2\left(x+11\right)-3\left(x+11\right)`