How do you factor by grouping: 3x^2 + 3 + x^3 + x?

2 Answers
Mar 13, 2018

The factored form of the expression is (x^2+1)(x+3).

Explanation:

First, rearrange the terms. Then, factor x^2 out from the first two terms and 1 out from the last two terms. Lastly, combine the two factors to get an answer:

color(white)=3x^2+3+x^3+x

=x^3+3x^2+x+3

=color(red)(x^2)*x+color(red)(x^2)*3+x+3

=color(red)(x^2)(x+3)+x+3

=color(red)(x^2)(x+3)+color(blue)1*x+color(blue)1*3

=color(red)(x^2)(x+3)+color(blue)1(x+3)

=(color(red)(x^2)+color(blue)1)(x+3)

Mar 13, 2018

This does it: (x+3)(x^2 + 1)

Explanation:

I am not sure about the "by grouping" method, but I stumbled on a way to factor that expression.

I noticed that it could be written 3*(x^2 +1) + x*(x^2 +1).

From there I put the 3 and the x inside a second set of parentheses and saw that

3x^2 + 3 + x^3+ x = (3+x)(x^2 + 1)

So (3+x)and(x^2 + 1) are the factors.

A preferable way to write it would probably be (x+3)(x^2 + 1).

I hope this helps,
Steve