tuesday, november 8 th set up a new assignment sheet 4.3: greatest common factors
TRANSCRIPT
Tuesday, November 8th Set up a new assignment
sheet
4.3: Greatest Common Factors
Greatest Common Factor (GCF)
• Factors – numbers, variables, monomials or polynomials multiplied to obtain a product
• Greatest Common Factor (GCF) – the greatest factor shared by two or more numbers, monomials, or polynomials
Greatest Common Factorsaka GCF’s
Find the GCF for each set of following numbers.Find means tell what the terms have in common.Hint: list the factors and find the greatest match.
a) 2, 6
b) -25, -40
c) 6, 18
d) 16, 32
e) 3, 8
2
-56
161
No common factors? GCF =1
Find the GCF for each set of following numbers.
Hint: list the factors and find the greatest match.
a) x, x2
b) x2, x3
c) xy, x2y
d) 2x3, 8x2
e) 3x3, 6x2
f) 4x2, 5y3
xx2
xy
2x2
Greatest Common Factorsaka GCF’s
3x2
1 No common factors? GCF =1
Find the GCF for each set of following numbers.
a) 2x + 4yb) 5a – 5bc) x – 6yd) 2m + 6mne) 5x2y – 10xyf) 10y3 + 20y2 - 5y g) -12 – 8x2
2
15
5xy
2m
Greatest Common Factorsaka GCF’s
5y
-4 Both negative? Factor -1
Factor out the GCF for each polynomial:Factor out means you need the GCF times the
remaining parts.
a) 2x + 4y
b) 5a – 5b
c) 18x – 6y
d) 2m + 6mn
e) 5x2y – 10xy
2(x + 2y)
6(3x – y)
5(a – b)
5xy(x - 2)
2m(1 + 3n)
Greatest Common Factorsaka GCF’s
How can you check? Distribute.
How can you check? Distribute.
a) 2x + 4y
b) 5a – 5b
c) 18x – 6y
d) 2m + 6mn
e) 5x2y – 10xy
2(x + 2y)
6(3x – y)
5(a – b)
5pq(p - 2)
2m(1 + 3n)
Greatest Common Factorsaka GCF’s
FACTORING by GCF
Take out the GCF EX:
15xy2 – 10x3y + 25xy3
How:
Find what is in common in each term and put in front. See what is left over.
Check answer by distributing out.
Solution:
5xy( )3y – 2x2 + 5y2
FACTORING
Take out the GCF EX:
2x4 – 8x3 + 4x2 – 6x
How:
Find what is in common in each term and put in front. See what is left over.
Check answer by distributing out.
Solution:
2x(x3 – 4x2 + 2x – 3)
When the directions say “factor”.
Always try taking out a GCF first.
the difference of Perfect Squares
x2 – 4 =
the answer will look like this: ( )( )
take the square root of each part:( x 2)(x 2)
Make 1 a plus and 1 a minus:(x + 2)(x - 2 )
the difference of Perfect Squares
9x2 – 25 =
the answer will look like this: ( )( )
take the square root of each part:(3x 5)(3x 5)
Make 1 a plus and 1 a minus:(3x + 5)(3x - 5)
FACTORING by GCF
Take out the GCF EX:
15xy2 – 10x3y + 25xy3
How:
Find what is in common in each term and put in front. See what is left over.
Check answer by distributing out.
Solution:
5xy( )3y – 2x2 + 5y2
FACTORING
Difference of Perfect
Squares
EX:
x2 – 64
How:
Take the square root of each part. One gets a + and one gets a -.
Check answer by FOIL.
Solution:
(x – 8)(x + 8)
Homework
Worksheet