Review all factoring techniques needed for Math 20-1. Alberta Grade 11 mathematics.
Lesson 1.6 of Quadratic Functions & Equations in Math 20-1 — Alberta curriculum lessons.
The big idea: find the GCF (greatest common factor) of all the terms, divide each term by the GCF, and write the result as a product.
The Three Steps. Step 1: Find the GCF of all the coefficients (the numbers).
Step 2: Find the GCF of each variable — use the lowest power of each variable that appears in every term.
Step 3: Pull the GCF out front and write what remains inside brackets.
Quick check: Multiply your answer back out — you should recover the original expression exactly.
When to use it: When there is no common factor across all terms, but you can group terms together that do share factors. This technique is most often used with four-term polynomials.
The Three Steps. Step 1: Group the first two terms together and the last two terms together.
Step 2: Factor the GCF out of each group.
Step 3: If the brackets match, factor the matching binomial out as a common factor.
Factor completely.
Step 1 — GCF of the Coefficients. Coefficients are 8, 6, 4.
GCF of 8, 6, 4 = 2.
Step 2 — GCF of Each Variable. Variable a: lowest power across all terms is a^1, so take a.
Variable b: lowest power across all terms is b^2, so take b^2.
Overall GCF: 2ab^2.
Step 3 — Divide and Write the Result. 8a^2b^3 ÷ 2ab^2 = 4ab
-6ab^2 ÷ 2ab^2 = -3
4ab^4 ÷ 2ab^2 = 2b^2
Answer: 2ab^2(4ab - 3 + 2b^2)
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