Factoring out a common factor
Factoring Out a Common Factor is the process of writing a polynomial as a product by identifying the largest factor common to all terms and using the distributive law in reverse. Covered in Yoshiwara Elementary Algebra Chapter 6: Quadratic Equations, this is the first step in any factoring problem for Grade 6 students and simplifies subsequent steps. The greatest common factor (GCF) is divided out of each term to produce the factored form.
Key Concepts
Property Factoring is the reverse of multiplying factors together. To factor an expression with a common factor, find the largest factor that divides into each term and use the distributive law in reverse. A common factor is an expression that is a factor of each term of another expression.
Examples To factor $10x^2 15x$, the largest common factor is $5x$. Dividing each term by $5x$ gives $2x$ and $ 3$. The factored form is $5x(2x 3)$.
In the expression $18y^2 + 24y$, the largest common factor is $6y$. Factoring this out gives $6y(3y + 4)$.
Common Questions
How do you factor out a common factor?
Find the largest factor (GCF) that divides into every term of the expression. Write the GCF outside parentheses and the remaining terms inside, then verify by distributing.
What is the GCF in factoring?
The GCF (greatest common factor) is the largest number and the highest power of each common variable that divides every term in the expression.
Why do we factor out the greatest common factor first?
Factoring out the GCF first simplifies the remaining expression, making it easier to apply other factoring techniques like factoring trinomials.
Where is factoring out a common factor in Yoshiwara Elementary Algebra?
This technique is introduced in Chapter 6: Quadratic Equations of Yoshiwara Elementary Algebra.
How do you check if you factored correctly?
Distribute the GCF back into the parentheses. If the result matches the original expression, the factoring is correct.