AFDA – Unit 5: Polynomials
Day 5 Notes: Factor By Grouping
Name: _________________
Block: _____ Date:_______
Follow these 5 Steps to Factor by Grouping:
Step 1: Decide if the four terms have anything in common, this is called the
_____________ ____________ _____________ or ____________. If so, Factor out
the GCF.
**Remember, a GCF can be an integer, variable, or combination of both
Step 2: Create __________ smaller groups within the problem; this is done by
grouping the first two terms together and the last two terms together.
Step 3: Factor out the ____________ from each of the two groups. (In the second
group, you have a choice of factoring out a __________ or ___________ number. To
determine whether you should factor out a positive or negative number, you need to
look at the signs before the ____________ and ____________ term. If the two signs
are the same, you need to factor out a _______________ number. If the two signs are
different, you must factor out a ________________ number.
Step 4: Combine your ______________ in one set of parenthesis and ____________
down your other set of parenthesis.
Step 5: Determine if the remaining factors can be factored any further.
** Use ONLY when there is a polynomial with ___________ terms.
Example: 𝑥 3 − 5𝑥 2 + 3𝑥 − 15
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Example: 3𝑥 3 − 6𝑥 2 + 15𝑥 − 30
**HINT: Look for a GCF
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Factor By Grouping:
𝑥 3 + 3𝑥 2 + 5𝑥 + 15
4𝑥 3 𝑦 + 4𝑥 2 𝑦 + 8𝑥𝑦 + 8𝑦
2𝑥 3 − 4𝑥 2 + 5𝑥 − 10
3𝑥 3 + 3𝑥 2 − 8𝑥 − 8
5𝑥 3 + 10𝑥 2 + 25𝑥 + 50
3𝑥 3 − 12𝑥 2 + 2𝑥 − 8
Now You Try!!
𝑥 3 𝑦 2 + 3𝑥 2 𝑦 2 + 4𝑥𝑦 2 + 12𝑦 2
𝑥 3 + 2𝑥 2 + 7𝑥 + 14
5𝑥 3 − 10𝑥 2 + 4𝑥 − 8
−4𝑥 3 − 12𝑥 2 − 6𝑥 − 18
5𝑥 4 + 5𝑥 3 + 25𝑥 2 + 25𝑥
𝑥 3 𝑦𝑧 + 3𝑥 2 𝑦𝑧 + 2𝑥𝑦𝑧 + 6𝑦𝑧