Table of contents

0. Review of Algebra4h 18m
1. Equations & Inequalities3h 18m
2. Graphs of Equations43m
3. Functions2h 17m
4. Polynomial Functions1h 44m
5. Rational Functions1h 23m
6. Exponential & Logarithmic Functions2h 28m
7. Systems of Equations & Matrices4h 6m
8. Conic Sections2h 23m
9. Sequences, Series, & Induction1h 22m
10. Combinatorics & Probability1h 45m

0. Review of Algebra

Factoring Polynomials

College Algebra

0. Review of Algebra

Factoring Polynomials

Previous problemNext problem

1:52 minutes

Problem 11

Textbook Question

Factor out the greatest common factor from each polynomial. See Example 1. 12m+60

Verified step by step guidance

Identify the coefficients and terms in the polynomial: 12m and 60.

Determine the greatest common factor (GCF) of the coefficients 12 and 60.

The GCF of 12 and 60 is 12, as it is the largest number that divides both 12 and 60.

Factor out the GCF from each term in the polynomial: 12m and 60.

Rewrite the polynomial as the product of the GCF and the simplified terms: 12(m + 5).

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above

Video duration:

Play a video:

Was this helpful?

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Greatest Common Factor (GCF)

The Greatest Common Factor (GCF) is the largest integer or algebraic expression that divides two or more numbers or terms without leaving a remainder. To find the GCF, one can list the factors of each term and identify the highest one that appears in all lists. For example, in the expression 12m + 60, the GCF is 12, as it is the largest factor common to both terms.

Factoring Polynomials

Factoring polynomials involves rewriting a polynomial as a product of its factors. This process simplifies expressions and can make solving equations easier. In the case of 12m + 60, factoring out the GCF (12) results in 12(m + 5), demonstrating how the polynomial can be expressed in a simpler form.

Distributive Property

The Distributive Property states that a(b + c) = ab + ac, allowing us to distribute a factor across terms within parentheses. This property is essential when factoring, as it helps verify the correctness of the factorization. After factoring 12 from 12m + 60, one can use the distributive property to expand back to the original expression, confirming that 12(m + 5) equals 12m + 60.