Question

Use the grouping method to factor x³ + x² + 3x+3.

A. (x²+1)(x+3)
B. x(x+3)(x + 1)
C. (x + 1)(x+3)
D. (x + 1)(x2+3)

Answer 1

D.
`(x + 1)(x^2 + 3)`

Explanation:

Hello!

We can group the first two terms and the last two terms.

Factor by Grouping

• 
  `x^2 + x^2 + 3x + 3`
• 
  `x^2(x + 1) + 3(x + 1)`
• 
  `(x^2 + 3)(x + 1)`

Factoring by grouping is the process of breaking down larger polynomials to smaller ones to factor. We can then combine like factors.

In the second step, we can see that we can rewrite
`x^3 + x^2` as
`x^2(x + 1)`, as both the two terms share a common factor of
`x^2`. We can pull out
`x^2` from that expression. Similarly,
`3x` and
`3` share a common factor of
`3`, so we can pull that out.