Factoring

04/20/23

Factoring Polynomials

Objective: factor a quadratic expression where the a term does not equal one.

2ax bx c

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

8

64 2

Ex.

10

75 2

Ex.

35

27 5

Ex.

10

35 2

Ex.

24

1012 2

Ex.

6

76 1

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.

30

Factor. Ex.

23 11 10x x

115 6

3x 3x

5 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.

5 6 30

5 6 11 3 10 30

3 5x 2x 3 5 2x x GCF 1

Notes

1) Factor out GCF.

24

Factor. Ex.

22 5 12x x

53 8

2x 2x

3 8

2) Magic X.

3) Magic T.

- Reduce?

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

1

44) You now have your factors.

3 8 24

3 8 5 2 12 24

2 3x 4x 2 3 4x x

GCF 1

Notes

1) Factor out GCF.

20

Factor. Ex.

22 9 10x x

94 5

2x 2x

4 5

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.

4 5 20

4 5 9 2 10 20

2x 2 5x 2 2 5x x

Now you try.

GCF 1

Notes

1) Factor out GCF.

24

Factor. Ex.

26 5 4x x

53 8

6x 6x

3 8

2) Magic X.

3) Magic T.

- Reduce?

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

2

14) You now have your factors.

3 8 24

3 8 5 6 4 24

2 1x 3 4x 2 1 3 4x x

3

4

GCF 1

Notes

1) Factor out GCF.

20

Factor. Ex.

210 2x x

14 5

10x 10x

4 5

2) Magic X.

3) Magic T.

- Reduce?

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

5

24) You now have your factors.

4 5 20

4 5 1 10 2 20

5 2x 2 1x 5 2 2 1x x

2

1

GCF 1

Notes

1) Factor out GCF.

48

Factor. Ex.

216 16 3x x

164 12

16x 16x

4 12

2) Magic X.

3) Magic T.

- Reduce?

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

4

1 4) You now have your factors.

4 12 48

4 12 16 16 3 48

4 1x 4 3x 4 1 4 3x x

4

3

Now you try.

GCF 1

Summary

To factor a quadratic first set up the Magic __. On top multiply ac and on _______ put b. Now find a pair of numbers that ________ to equal the top and ____ to equal the bottom. Next set up your ______ T. Put ax on the top and put your pair on the bottom. Reduce if possible.

Xbottom

multiplyadd Magic

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. 22 7 6x 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

HomeworkFactor.

21. 4 11 6x x 22. 3 5 12x x

23. 2 7 5x x 24. 8 13 6x x

25. 4 8 3x x 26. 6 7 2x x

27. 6 5 6x x 28. 8 6 9x x

29. 12 13 4x x 210. 10 7 12x x