Bell Work 4//2015Factor.

21. 25 20 4x x

22. 81x 23. 49 36x

GCF

GCF GCF

1

1 1

Yesterday’s Homework

1. Any questions?2. Please pass your homework to the front.

• Make sure the correct heading is on your paper.• Is your NAME on your paper?

• Make sure the homework is 100% complete.• Incomplete work will NOT be accepted.

Choosing a Factoring Method

04/21/23

Heading

Today we will factor out the GCF first, and then factor the remaining quadratic expression.

8.6

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• Magic X

24

24 6

Ex.

24

24 6

Ex.

24

104 6

Ex.

24

104 6

Ex.

30

15 6

Ex.

36

06 6

Ex.

Notes• Steps for Factoring a Quadratic Equation

1) Factor out the GCF (if possible)

2) Set up the Magic X.

• Find the pair that multiplies to equal the top, and adds up to equal the bottom.

3) Set up the Magic T.• Put ax on the top two, and the pair we found for the bottom two.• Treat each side as a fraction and reduce if possible

4) You now have your factors.

2ax bx c

a c

b1# 2#

ax ax

1# 2#

• ac goes on top, and b goes on bottom

Notes

1) Factor out GCF.

40

Factor. Ex.

3 24 3 10x x x

35 8

4x 4x

5 8

2) Magic X.

3) Magic T.

- Reduce?

- What pair multiplies to equal top and adds to equal the bottom?

1

2 4) You now have your factors.

5 8 40

5 8 3 4 10 40

x 4 5x 2x 4 5 2x x x

x 24x 3xGCF x

10

Notes

1) Factor out GCF.

24

Factor. Ex.

215 10 40x x

24 6

3x 3x

4 6

2) Magic X.

3) Magic T.

- Reduce?

- What pair multiplies to equal top and adds to equal the bottom?

1

24) You now have your factors.

4 6 24

4 6 2 3 8 24

5 3 4x 2x 5 3 4 2x x

5 23x 2x

GCF 5

8

Now you try.

Notes

1) Factor out GCF.

16

Factor. Ex.

23 24 48x x

84 4

x x

4 4

2) Magic X.

3) Magic T.

- Reduce?

- What pair multiplies to equal top and adds to equal the bottom?

4) You now have your factors.

4 4 16

4 4 8 1 16 16

3 4x 4x

23 4x

3 2x 8xGCF 3

16

NotesFactor.

Ex.350 18x x

2x 225x 9GCF 2

2x 5x 5x 3 3

5x 5x3 3 2 5 3 5 3x x x

Ex.2360 490x

10 236x 49GCF 10

10 6x 6x 7 7

6x 6x7 7 10 6 7 6 7x x

Now you try.

x

Summary

Write a summary about today’s lesson.

When first factoring take out the greatest common ______ if possible. After that do the Magic __ and Magic __. Look to see if it is a _________ of two squares to use the short cut.

factor XT difference

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. 3 24 5 6x x x

Today’s Homework

1. Pencil ONLY.2. Must show all of your work.• NO WORK = NO CREDIT

3. Must attempt EVERY problem.4. Always check your answers.

Rules for Homework

Homework 8.6Factor.

21. 4 12 40x x 3 22. 7 12x x x

3 23. 2 6x x x 24. 15 50 40x x

3 25. 2 10 12x x x 3 26. 6 33 18x x x

27. 6 24 24x x 3 28. 9 6x x x

39. 49x x 210. 640 810x