7.1 continued
December 16, 2013
Factoring a Number
24
Prime Number: Factoring a number completely:
7.1 continued
December 16, 2013
GREATEST COMMON FACTOR (GCF)
36, 48, 120
GCF of Monomials
10x3, 15x5
7.1 continued
December 16, 2013
Determining the GCF of Two or more Monomials
1. Determine the GCF of the numerical coefficients
2. Determine the smallest exponent for each base that each monomial has in common
3. The product of steps 1 and 2 is the GCF of the monomials
EXAMPLES
6y4, 9y6
75x3y4, 45x2y5, 225x4y7
Whenever you find the GCF, or find a factor, you can write the original as a product of the factors. 75x3y4=
45x2y5=
225x4y7=
7.1 continued
December 16, 2013
MORE PRACTICE
Common Factors in Polynomials
To factor a polynomial, we write the polynomial as a product of two or more polynomials. 24 = 12*2
24 = 6*2*2
24= 3*2*2*2
The first step (always) is to determine whether all of the terms have a GCF greater than 1
7.1 continued
December 16, 2013
Distributive Property
2(x+1)
Factoring out a GCF is the opposite of the distributive property!
4x­2
6x2+3x
12x3­20x2
7.1 continued
December 16, 2013
ONLY FACTOR IF THE RESULTING POLYNOMIAL HAS INTEGER COEFFICIENTS!
Factoring out a GCF from a polynomial
1. Find the GCF of the terms
2. Factor each term with the GCF as one factor
3. Apply the distributive property backwards
4. Multiply back in to check your answer.
7.1 continued
December 16, 2013
More Practice
1. 10x3­5x2
2. ­4x3­8y2
3. ­12x2y3 + 10xy3
4. 54x3y5 + 36x4y2 ­ 90x6y3
3x(x+4) ­y(x+4)
5(2x­1) ­2y(2x­1) +z(2x­1)
x2(x+5) +3x4+(x+5) ­6x3(x+5)
7.1 continued
December 16, 2013
Factor by Grouping
x3 ­ 3x2 + 2x ­ 6
Factor by Grouping
1. Put in descending order
2. Group the first 2 terms and the last 2 terms
3. Factor the GCF in each group
4. If there is a common binomial factor, factor that out. 7.1 continued
December 16, 2013
ax+bx+ay +by
2x3 ­ 8x2 + 5x ­ 20
x3 + 2x2 ­ 5x ­ 10