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All courses Math III · A-SSE.2 16 of 55
Use expression structure to find useful rewrites.

Factor a polynomial by grouping to reveal a common binomial or polynomial factor

Problem
Factor this higher-degree polynomial by grouping: x³+2x²+3x+6
Your answer
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Hint

Group the first two terms and the last two terms, then look for a common binomial factor.

Factoring by grouping works when each pair has a common factor and both groups simplify to the same remaining expression.

Solution walkthrough

01

Group the polynomial into pairs

\[(x^3+2x^2)+(3x+6)\]

Grouping the first two and last two terms sets up a shared-binomial pattern.

02

Factor each group

\[x^2(x+2)+3(x+2)\]

The first group factors out \(x^2\), and the second group factors out \(3\).

03

Factor out the common binomial

\[(x+2)(x^2+3)\]

Now both terms contain the common factor \((x+2)\), so it can be factored out.

04

State the factorization

\[x^3+2x^2+3x+6~=~(x+2)(x^2+3)\]

So the polynomial factors by grouping as \((x+2)(x^2+3)\).

05

State the final answer

\[\text{The}~\text{factorization}~\text{is}~(x+2)(x^2+3).\]

The factorization is \((x+2)(x^2+3)\).

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Another way

  1. You can check by expansion: \((x+2)(x^2+3)=x^3+2x^2+3x+6\).

!

Common mistake

A common mistake is to stop at \(x^2(x+2)+3(x+2)\) and forget the final step of factoring out the shared binomial \((x+2)\).