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Greatest Commen Factor
Find the GCF
8x2 – 2x
1. Find the largest number that will divide into all the coefficients evenly.
Coefficients – 8, 2
The largest number that will divide into both of them is 2.
2. Find the largest variable that will into all the coefficients evenly.
*choose the variable with the smallest exponent*
The largest variable that will go into both of them is x.
3. Put both of them together.
GCF = 2x
Factoring
· Factoring is the opposite of
expanding and simplify. It means
to write as a product.
Expanding
(x + 2) (x – 2) à x2 – 4
3 x 2 àààà 6
Factoring
X2 – 4 à(x + 2) (x – 2)
6 ààà3 x 2
6y3 – 24y2
The easiest way to factor is to find the GCF.
GCF : 6y2
1. Find the GCF .
2. Wright down the GCF and open the Brackets.
3. Divide the polynomial by GCF and check the brackets.
4. Check by expanding.
6y3 – 24y2
1. GCF : 6y2
2. 6y2(
3. 6y2(y – 4)
4. 6y2(y – 4)
6y3 – 24y2
Product & Sum
Find two numbers that:
Add to give you 8: 2 + 6 = 8
Multiply to give you 12: 2 x6 = 12
Factoring Trinomials
Factor 6x2 + 3x + 9 6x2 + 3x + 9
3(2x2 + 8x +12)
GCF: 3
Factor x2 +8x +12
1(x2 +8x +12)
GCF: 1 We cannot factor this trinomial
by simply finding the GCF.
This is another way of factor
x2 +8x +12 – product The next step is to
Find 2 numbers that have place those numbers in
a sum = 8 brackets.
a product = 12 (x + 2)(x + 6)
The number are x2 + 6x + 2x + 12
2 & 6 x2 + 8x + 12