Example Card：Factoring an Expression Using a Common Factor
Grade 8 math lesson on factoring algebraic expressions using the greatest common factor (GCF). Students learn to identify common factors among terms, factor them out using the distributive property in reverse, and verify their factoring by expanding.
Key Concepts
Let’s flip the script: can you spot what’s shared and, like a math magician, tuck it outside?
Example Problem : Factor: $8x + 12$.
Step by Step: 1. Look for a number that divides evenly into both $8x$ and $12$. That’s our common factor. 2. $8x$ can be written as $4 \times 2x$ and $12$ as $4 \times 3$. 3. Using the distributive property in reverse (factoring), write: $4(2x) + 4(3) = 4(2x + 3)$. 4. So, $8x + 12 = 4(2x + 3)$.
Common Questions
How do you factor an expression using a common factor?
Find the greatest common factor (GCF) of all terms in the expression, then factor it out. For example, 6x + 9 has GCF of 3, so it factors to 3(2x + 3). Check by distributing: 3 x 2x + 3 x 3 = 6x + 9.
What is the greatest common factor in algebra?
The GCF is the largest factor that divides evenly into all terms of an expression. For 12x and 8, the GCF is 4 because 4 divides both 12 and 8. So 12x + 8 = 4(3x + 2).
How does factoring relate to the distributive property?
Factoring is the reverse of the distributive property. Distributing expands: 3(2x+1) = 6x+3. Factoring compresses: 6x+3 = 3(2x+1). They are opposite processes.
How do you check if you factored correctly?
To verify factoring, distribute the factored expression back out using the distributive property. If the result matches the original expression, the factoring is correct.