1. Tuesday, November 8 th Set up a new assignment sheet 4.3: Greatest Common Factors

2. 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

3. Greatest Common Factors aka 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 -5 6 16 1 No common factors? GCF =1

4. Find the GCF for each set of following numbers. Hint: list the factors and find the greatest match. a)x, x 2 b)x 2, x 3 c)xy, x 2 y d)2x 3, 8x 2 e)3x 3, 6x 2 f)4x 2, 5y 3 x x2x2 xy 2x 2 Greatest Common Factors aka GCF’s 3x 2 1 No common factors? GCF =1

5. Find the GCF for each set of following numbers. a)2x + 4y b)5a – 5b c)x – 6y d)2m + 6mn e)5x 2 y – 10xy f)10y 3 + 20y 2 - 5y g)-12 – 8x 2 2 1 5 5xy 2m Greatest Common Factors aka GCF’s 5y -4Both negative? Factor -1

6. 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)5x 2 y – 10xy 2(x + 2y) 6(3x – y) 5(a – b) 5xy(x - 2) 2m(1 + 3n) Greatest Common Factors aka GCF’s How can you check? Distribute.

7. How can you check? Distribute. a)2x + 4y b)5a – 5b c)18x – 6y d)2m + 6mn e)5x 2 y – 10xy 2(x + 2y) 6(3x – y) 5(a – b) 5pq(p - 2) 2m(1 + 3n) Greatest Common Factors aka GCF’s

8. FACTORING by GCF Take out the GCFEX: 15xy 2 – 10x 3 y + 25xy 3 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 – 2x 2 + 5y 2

9. FACTORING Take out the GCFEX: 2x 4 – 8x 3 + 4x 2 – 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(x 3 – 4x 2 + 2x – 3)

10. When the directions say “factor”. Always try taking out a GCF first.

11. the difference of Perfect Squares x 2 – 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 )

12. the difference of Perfect Squares 9x 2 – 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)

13. FACTORING by GCF Take out the GCFEX: 15xy 2 – 10x 3 y + 25xy 3 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 – 2x 2 + 5y 2

14. FACTORING Difference of Perfect Squares EX: x 2 – 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)

15. Homework Worksheet