Monday’s Homework

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

• Incomplete work will NOT be accepted.

Factoring

04/24/23Polynomial Factoring

Objective: factor a quadratic expression where the a term equals one.

2x 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

30

115 6

Ex.

14

52 7

Ex.

12

42 6

Ex.

21

103 7

Ex.

5

61 5

Ex.

8

91 8

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.

14

Factor. Ex.

2 9 14x x

92 7

x x

2 7

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.

2 7 14

2 7 9 1 14 14

2x 7x 2 7x x

GCF 1

Notes

1) Factor out GCF.

27

Factor. Ex.

2 6 27x x

63 9

x x

3 9

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.

3 9 27

3 9 6 1 27 27

3x 9x 3 9x x

Now you try.

GCF 1

Notes

1) Factor out GCF.

42

Factor. Ex.

2 42x x

16 7

x x

6 7

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.

6 7 42

6 7 1 1 42 42

6x 7x 6 7x x

GCF 1

Notes

1) Factor out GCF.

36

Factor. Ex.

2 15 36x x

153 12

x x

3 12

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.

3 12 36

3 12 15 1 36 36

3x 12x 3 12x x

Now you try.

GCF 1

Summary

Write a summary about today’s lesson. To factor a quadratic with no a first set up the

______ X. On top put c and on bottom put __. Now find a pair of numbers that multiply to equal the ____ and add to equal the _______. Next set up your Magic __. Put x on the top and put your pair on the bottom.

Magic btop

bottom T

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. 8 15x x 22. 2 35x x 23. 6 27x x

24. 10 24x x 25. 6 7x x 26. 7 8x x

27. 13 36x x 28. 30x x 29. 12x x

210. 3 40x x 211. 12 27x x 212. 8 20x x

213. 5 66x x 214. 8 48x x 215. 90x x

Complete the Ticket Out the Door without talking!!!!!Talking = NO CREDIT!

Ticket Out the Door

Put your NAME on the paper.When finished, turn your paper face DOWN.

Factor. 2 4 32x x

8 4x x