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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.

2, 6

-25, -40

6, 18

16, 32

3, 8

2

-5

6

16

1

No common factors? GCF =1

Find the GCF for each set of following numbers.

Hint: list the factors and find the greatest match.

x, x2

x2, x3

xy, x2y

2x3, 8x2

3x3, 6x2

4x2, 5y3

Greatest Common Factorsaka GCF’s

x

x2

xy

2x2

3x2

1

No common factors? GCF =1

Find the GCF for each set of following numbers.

a) 2x + 4y

5a – 5b

x – 6y

2m + 6mn

5x2y – 10xy

10y3 + 20y2 - 5y

-12 – 8x2

Greatest Common Factorsaka GCF’s

2

5

1

2m

5xy

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

5a – 5b

18x – 6y

2m + 6mn

5x2y – 10xy

Greatest Common Factorsaka GCF’s

2(x + 2y)

How can you check?

Distribute.

5(a – b)

6(3x – y)

2m(1 + 3n)

5xy(x - 2)

How can you check? Distribute.

a) 2x + 4y

5a – 5b

18x – 6y

2m + 6mn

5x2y – 10xy

Greatest Common Factorsaka GCF’s

2(x + 2y)

5(a – b)

6(3x – y)

2m(1 + 3n)

5pq(p - 2)

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

(x – 8)(x + 8)

Homework

Worksheet

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