5.2: Greatest Common Factor | Algebra 1 Honors

How it works

Factoring reverses multiplication. Begin by finding the greatest common factor shared by all terms, including both numeric and variable factors. Dividing each term by that factor produces the remaining expression. Expand the result to verify the factorization.

ab+ac=a(b+c)

Worked examples

Example 1

Factor $\displaystyle 6x^3+9x^2$ .

The greatest common factor is $\displaystyle 3x^2$ . Thus $\displaystyle 6x^3+9x^2=3x^2(2x+3)$ .

Example 2

Factor $\displaystyle -4x^2+12x$ using a negative common factor.

Factor out $\displaystyle -4x$ : $\displaystyle -4x(x-3)$ . Expanding gives the original expression.

Problems

Problem 5.2.1

Factor $\displaystyle 10x^2+15x$ .

Show worked solution

The greatest common factor is $\displaystyle 5x$ , so the result is $\displaystyle 5x(2x+3)$ .

Problem 5.2.2

Factor $\displaystyle 8a^3b-12a^2b^2$ .

Show worked solution

The common factor is $\displaystyle 4a^2b$ . The result is $\displaystyle 4a^2b(2a-3b)$ .

Problem 5.2.3

Factor $\displaystyle 3x^2-27$ completely.

Show worked solution

First factor out $\displaystyle 3$ : $\displaystyle 3(x^2-9)$ . Then use a difference of squares: $\displaystyle 3(x-3)(x+3)$ .

Lesson Problems PDF Solutions PDF Unit MCQ

How it works

Worked examples

Example 1

Example 2

Problems

Problem 5.2.1

Problem 5.2.2

Problem 5.2.3

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