AFDA – Unit 5: Polynomial
Day 1 Notes: GCF and FOILing/EWE
Name: _________________
Block: _____ Date:_______
Today we will…
 find the greatest common factor (GCF) of terms
 distribute factors (FOIL/EWE)
First step in Factoring
**Finding your Greatest Common Factor**
What’s a factor?
What is a GCF?
Factoring out the GCF…
1. Determine the GCF
2. Factor (divide out) the GCF from each term.
1. 49𝑎 − 7
2. 16𝑏 − 4
3. 3𝑎 − 9
4. 11𝑐 2 + 33𝑐
5. 12𝑑𝑒 − 15𝑑
6. 16𝑏𝑐 − 8𝑏
Finding the Greatest Common Factor (GCF) in the Calculator
1. Press MATH to access the menu
2. Scroll right to access the NUM submenu
3. Select 9: gcd(
**gcd means greatest common divisor
If finding the GCF of two numbers… 𝑔𝑐𝑑(#, #) ENTER
If finding the GCF of three numbers… 𝑔𝑐𝑑(#, 𝑔𝑐𝑑(#, # ENTER
Common Error Conditions
 ERR:ARGUMENT if you forgot a comma
 ERR:DOMAIN if the numbers aren’t positive integers
4. 18𝑔2 ℎ − 30𝑔ℎ2
5. 18𝑝𝑤 3 + 24𝑤 2 − 12𝑝
6. 40𝑗 3 𝑘 3 − 60𝑗 2 𝑘 4 + 20𝑗𝑘 5
7. 15𝑚3 𝑛3 − 7𝑚𝑛2 − 22𝑚4 𝑛5
8. 12𝑝10 𝑚8 + 36𝑝8 𝑚6 − 48𝑝6 𝑚4 + 144𝑝4 𝑚2
FOILing and EWE
FOILing = First Outer Inner Last
and
EWE = Each With Each
4(𝑥 − 2)
−2(3𝑥 + 4)
−3𝑥(𝑥 − 5)
5𝑥(2𝑥 − 4)
4𝑏(3𝑐 − 2)
6𝑔ℎ(3𝑔 − 5ℎ)
5(𝑥 2 − 2𝑥 + 6)
−(𝑥 2 + 7𝑥 − 10)
8𝑒(3𝑒 2 + 𝑒 − 8)
2𝑥(6𝑥 2 + 𝑥 − 7)
(𝑐 + 1)(𝑐 + 7)
(𝑏 − 1)(𝑏 + 4)
(𝑑 + 2)2
(𝑓 − 6)2
(2𝑧 + 1)(𝑧 + 2)
(3𝑥 + 2)(𝑥 − 4)
𝑠(2𝑠 + 3)(3𝑠 + 2)
𝑟(6𝑟 − 5)(2𝑟 + 3)
(𝑥 + 1)(𝑥 2 + 3𝑥 + 5)
(𝑥 + 3)(𝑥 2 − 4𝑥 − 2)
The dimension of a rectangle are 𝑥 + 3 and 𝑥 + 2. Write an expression in standard
form representing the area of the rectangle.
The area of another rectangle is represented as 6𝑥 3 + 9𝑥 2 + 12𝑥 with the width
represented by the expression 3𝑥. What expression represents the length?