Friday’s Homework

1. Any questions?2. Make sure the homework is 100% complete.

• Incomplete work will NOT be accepted.

Factoring by GCF

04/22/23

Factoring Polynomials

Objective: factor polynomials by taking out the GCF.

Students apply basic factoring techniques to second-and simple third-degree polynomials. These techniques include finding a common factor for all terms in a polynomial, recognizing the difference of two squares, and recognizing perfect squares of binomials.

Notes

• Prime Factorization= All of the prime factors of a number.

• Hockey Stick Method1. Write an upside-down division sign.

2. Determine a prime-factor (2, 3, 5, 7, 11,…).

3. Write the factor in front of the division sign and place the quotient below.

4. Repeat until complete.

5. Write the prime factorization (the hockey stick).

• Prime Number= a whole number greater than 1 that has exactly two whole numbers as factors, itself and 1.

• 2, 3, 5, 7, 11, …

NotesWrite the prime factorization.

Ex.

60 - Upside Down Division- Try 2, 3, 5, 7, 11, …

23021535

- Anything else?

- Draw Hockey Stick

22 3 5PF

Ex.

84 - Upside Down Division- Try 2, 3, 5, 7, 11, …

24222137

- Anything else?

- Draw Hockey Stick

22 3 7PF

Ex.

9024531535

22 3 5PF

Now you try.

Notes• Greatest Common Factor (GCF)

= the highest factor of two or more numbers.

Find the GCF. Ex.

24 and 30

2

6GCF

24 303 12 15

4 5

Ex.18 and 45

3

9GCF

18 453 6 15

2 5

Ex.20 and 36

2

4GCF

20 362 10 18

5 9

Now you try.

Notes• Recall

• Distributive Property

a b c( )ab ac

a b c( )ab ac

When we distribute, all we are doing is multiplying whatever is outside the parenthesis with what is inside.

Distribution changes a multiplication problem into an addition or subtraction problem.

Notes• Factoring by GCF

• Distributive Property BACKWARDS

When we factor, all we are doing is pulling out the GCF of all terms inside the parenthesis.

ab ac a b c

ab ac a b c

Factoring changes an addition/subtraction problem into a multiplication problem.

NotesFactor.

Ex.23 6x x

3 23x 6xx 2x 2x

x 2

3x x 2 3 2x x

This takes too long.

Lets take off the training wheels.

Ex.23 6x x

3x x 2 3 2x x

What is the GCF?

GCF 3 What number goes in both?

x

What letter goes in both?

Now take out GCF.

What is left?

NotesFactor.

Ex.8 12x

4 2x 3 4 2 3x

What is the GCF?

GCF 4 What number goes in both?

What letter goes in both?

Now take out GCF.

What is left?

Ex.27 9x x

x 7x 9 7 9x x

What is the GCF?

GCF What number goes in both?

x

What letter goes in both?

Now take out GCF.

What is left?

Ex.25 20x x

5x x 4 5 4x x

GCF 5x

Ex.12 30x

6 2x 5 6 2 5x GCF 6

Ex.34 5x x

x 24x 5 24 5x x GCF x

Ex.24 28x x

4x x 7 4 7x x GCF 4x

Now you try.

NotesFactor.

Now you try.

Ex.26 9 12x x

3 22x 3x

GCF 3

4 23 2 3 4x x

Ex.3 22 6 10x x x

2x 2x 3x

GCF 2x

5 22 3 5x x x

Ex.3 24 8 9x x x

x 24x 8x

GCF x

9 24 8 9x x x

Ex.3 28 12 16x x x

4x 22x 3x

GCF 4 x

4 24 2 3 4x x x

NotesFactor.

Now you try.

Ex.8 4x

4 2x 1 4 2 1x

GCF 4

Ex.10 14x

2 5x 7 2 5 7x

GCF 2

Ex.5 4 26 15 21x x x

23x 32x 25x

GCF 3 2x

7 2 3 23 2 5 7x x x

Ex.215 5x

5 23x 1 25 3 1x

GCF 5

Ex.9 15x

3 3x 5 3 3 5x

GCF 3

Ex.5 310 20 45x x x

5x 42x 24x

GCF 5x

9 4 25 2 4 9x x x

Summary

The first option to factoring is to take out the _____. Find out which ________ and/or which ________ goes into every term in the parenthesis. Once you find the GCF then take it ____. Last keep inside the ___________ whatever is left-over.

GCF numbervariable

outparenthesis

Today’s Homework

1. Pencil ONLY.2. Must show all of your work.

• NO WORK = NO CREDIT3. Must attempt EVERY problem.4. Always check your answers.

Rules for Homework

Homework

1. 5 15x 2. 6 10x 23. 4 7x x

24. 2 6x x 25. 8 12x x 26. 3 6 6x x

27. 6 8 12x x 3 28. 7 5 4x x x 3 29. 4 16 12x x x

3 210. 4 8 6x x x 11. 6 3x

Factor.

212. 16 8x

13. 3 12x 214. 8 12x x 5 3 215. 2 4 5x x x

Complete the Ticket Out the Door without talking!!!!!

Talking = time after the bell!

Ticket Out the Door

Put your NAME on the paper.

When finished, turn your paper face DOWN.

Factor. 24 12 8x x

24 3 2x x