H. Algebra 2
Notes
Factoring
Date: ____________
What is factoring? Factoring is the reverse of _________________________.
Terms with Common Factors: Sometimes it is necessary to look for common factors in terms. When
we have factored out all the common factors we have factored out the greatest common factor (GCF).
Example. 4𝑦 2 − 8 = ______________________
= ______________________
Your Turn.
1) 5𝑥 4 − 20𝑥 3
2) 6𝑥 2 𝑦 − 21𝑥 3 𝑦 2 + 3𝑥 2 𝑦 3
Special Cases in Factoring
Trinomial Squares or Perfect Square Trinomials - Squares of binomials (yesterday) are also called
trinomial squares
𝑨𝟐 + 𝟐𝑨𝑩 + 𝑩𝟐 = (𝑨 + 𝑩)𝟐
𝑎𝑛𝑑
𝑨𝟐 − 𝟐𝑨𝑩 + 𝑩𝟐 = (𝑨 − 𝑩)𝟐
Example. 𝑥 2 − 10𝑥 + 25 = ______________________________
Your turn:
3) 9𝑦 2 + 25 − 30𝑦
4) 4𝑥 2 + 4𝑥 + 1
Difference of Squares Binomals – Multiplying opposite binomials results in a difference of squares.
𝐴2 − 𝐵 2 = (𝐴 + 𝐵)(𝐴 − 𝐵)
Example. 𝑥 2 − 9 = (𝑥 + 3)(𝑥 − 3)
Your turn:
5) 36𝑥 4 − 16𝑦 2
H. Algebra 2
Notes
Factoring Methods
Factoring by Grouping -Sometimes an expression of four or more terms can be grouped so that
common factors can be found. The common factor may be a binomial.
Example. 𝑦 2 + 3𝑦 + 4𝑦 + 12 = (𝑦 2 + 3𝑦) + (4𝑦 + 12)
= 𝑦(𝑦 + 3) + 4(𝑦 + 3)
= (𝑦 + 3)(𝑦 + 4)
Your turn:
6) 4𝑥 2 − 3𝑥 + 20𝑥 − 15
More Practice: (Hint: Look for GCF first)
7) 5𝑥 2 − 20
8) 𝑥 2 + 𝑥 − 6𝑥 − 6
9) 20𝑦 2 + 100𝑦 + 125
10) 3𝑥 2 + 18𝑥 − 27