How to Factor the Expression Using the GCF
You will see quite a few problems on your exam that ask you to factor the expression using the GCF.
Factor the Expression Using the GCF – Quiz
Instructions: Here is a quiz with questions that ask you to factor the expression using the GCF. If you want to see the examples on how to factor an expression using the GCF first, please look at the examples below the quiz.
| [WpProQuiz 11] |
What are Algebraic Expressions?
To factor the expression using the GCF, you first need to understand algebraic expressions.
Algebraic expressions are math problems that have terms that contain both numbers and variables.
For example, 5ab + 15b + 10bc is an algebraic expression.
We factor the above expression by taking out the variables and numbers that are common to each term of the expression.
The numbers that are multiplied by a variable are called coefficients.
How to Factor the Expression Using the GCF – Example
Our example expression is: 5ab + 15b + 10bc
In our example expression, 5ab is the first term, 15b is the second term, and 10bc is the third term.
Each term contains the variable b, so we can factor out this variable.
STEP 1: Multiply out each term to isolate the common variable or variables.
5ab + 15b + 10bc =
(5 × a × b) + (15 × b) + (10 × b × c)
So, each term has the variable b.
STEP 2: Expand the multiplication of the numbers in order to find the common coefficient.
(5 × a × b) + (15 × b) + (10 × b × c) =
(5 × a × b) + [(5 × 3) × b] + [(5 × 2) × b × c]
From the expanded expression, we can easily see that each term has a coefficient of 5.
STEP 3: Place the common factor at the front of each expanded term.
(5 × a × b) + [(5 × 3) × b] + [(5 × 2) × b × c] =
[5b(a)] + [5b(3)] + [5b(2 × c)]
STEP 4: Place the greatest common factor at the front of the new expression.
[5b(a)] + [5b(3)] + [5b(2 × c)] =
5b[a + (3) + (2 × c)] =
5b(a + 3 + 2c) =
5b(a + 2c + 3)
Other Practice Problems
In previous posts, we have looked finding the greatest common factor and exponent laws.
The exercises on other posts in this blog are advanced-level problems that require knowledge of all of these skills.
So, you should look at the following posts before you attempt the advanced math problems.
Finding the greatest common factor
You should also look at our posts on factoring quadratics and FOIL.
Go to the Next Exercise
