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Algebra basics (ASL)

Course: Algebra basics (ASL) > Unit 7

Lesson 4: Factoring polynomials by taking common factors (ASL)
Math
Algebra basics (ASL)
Quadratics and polynomials (ASL)
Factoring polynomials by taking common factors (ASL)
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Factoring by common factor review

Google Classroom
The expression 6m+15 can be factored into 3(2m+5) using the distributive property. More complex expressions like 44k^5-66k^4 can be factored in much the same way. This article provides a couple of examples and gives you a chance to try it yourself.

Example 1

Factor.
6, m, plus, 15
Both terms share a common factor of start color #e07d10, 3, end color #e07d10, so we factor out the start color #e07d10, 3, end color #e07d10 using the distributive property:
6m+15=3(2m+5)\begin{aligned} &6m+15\\\\ =&\goldD{3}(2m+5) \end{aligned}
Want a more in-depth explanation? Check out this video.

Example 2

Factor out the greatest common monomial.
44, k, start superscript, 5, end superscript, minus, 66, k, start superscript, 4, end superscript, plus, 77, k, cubed
The coefficients are 44, comma, 66, comma and 77, and their greatest common factor is start color #11accd, 11, end color #11accd.
The variables are k, start superscript, 5, end superscript, comma, k, start superscript, 4, end superscript, comma and k, cubed, and their greatest common factor is start color #11accd, k, cubed, end color #11accd.
Therefore, the greatest common monomial factor is start color #11accd, 11, k, cubed, end color #11accd.
Factoring, we get:
44k5−66k4+77k3=11k3(4k2)+11k3(−6k)+11k3(7)=11k3(4k2−6k+7)\begin{aligned} &44k^5-66k^4+77k^3\\\\ =&\blueD{11k^3}(4k^2)+\blueD{11k^3}(-6k)+\blueD{11k^3}(7)\\\\ =&\blueD{11k^3}(4k^2-6k+7) \end{aligned}
Want another example like this one? Check out this video.

Practice

Factor the polynomial below by its greatest common monomial factor.
3, b, start superscript, 5, end superscript, plus, 15, b, start superscript, 4, end superscript, minus, 18, b, start superscript, 7, end superscript, equals

Want more practice? Check out this exercise.