Factoring Activity 3.09

Greatest Common
Factor(GCF)
 Let’s try and factor 3x^3 + 27x^2 + 9x
 List the factors and find the GCF from
that each has in common.
3- 1 and 3
27- 1,3,9, and 27
9- 1,3, and 9
 They all have 3 in common.

Greatest Common
Factor(GCF)
 Put the GCF on the out side a pair of
parentheses: 3x()
 Divide the GCF from each of the
expressions.
3x^3÷3x x^2
27x^2÷ 3x  9x
9x÷ 3x  3
 3x(x^2+9x+3)

Special Products
 A binomial is considered a difference of
squares when both of the terms are perfect
squares
 a +/- b= (a - b)( a+ b)
 x^2 - 25
Both x^2 and 25 are perfect squares
 The square root of x^2 is x and the square
root of 25 is five
 (x-5)(x+5)

Factoring Trinomials
 -m^2-10m-16
 First you need to find the GCF and take
it out. Here it’s -1
-(m^2+10m+16)
 Now it’s time to find the factors
 -(m+ )(m+ )
 Factors of 10 and 16, let’s try 8 and 2

Factoring Trinomials
 -(m+8)(m+2)
FOILING gives us the original problem.

Factoring by Grouping
 x^3 − 3x^2 + 9x − 27
 There is no GCF between the four. So you
have to split them
 (x^3-3x^2) and (9x-27)
With the first the GCF you can take out is x^2.
x^2(-3 + x) . The second one you can take out
9. 9(x-3)
 X^2(x-3)+9(x-3)
 (x^2+9)

Sum and Difference of Cubes
 The formulas for this are
a3 + b3 = (a + b)(a2 – ab + b2)
a3 – b3 = (a – b)(a2 + ab + b2)
 Let’s try factoring x^15 – 64
 The cubed roots are x^15 and 4
respectively.
 Use the formula

Sum and Difference of Cubes
a3 – b3 = (a – b)(a2 + ab + b2)
 x^15 – 64= (x^5-4)(x^10+4x^5+16)
 So your factor would be
(x^5-4)

Factoring Activity 3.09

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Factoring Activity 3.09