CANDY CRUSH RULES!Work through the problem on your individual white

board. Show your work!After time is called, 5 students will randomly be

selected to provide their answer.When your name is called, stand up. (No more

writing allowed!)After all five students are standing, you will be asked

to show your solution.If you are correct, you get a candy!If you are incorrect, you don’t get a candy!

(2 𝑥3−4 𝑥+1 )+3(5 𝑥3−2𝑥+5)

1Polynomial Operations

and Combining Like Terms

𝟐 𝒙𝟑−𝟒 𝒙+𝟏+𝟏𝟓𝒙𝟑−𝟔 𝒙+𝟏𝟓

𝟏𝟕𝒙𝟑−𝟏𝟎𝒙+𝟏𝟔

Drop ParenthesisDistribute the 3

Combine Like Terms

Write in Descending Order

2 (4 𝑥2−𝑥+2 )−3 (𝑥3+3 𝑥−1)

Polynomial Operationsand Combining Like Terms

2

𝟖 𝒙𝟐−𝟐 𝒙+𝟒−𝟑 𝒙𝟑−𝟗 𝒙+𝟑

−𝟑 𝒙𝟑+𝟖 𝒙𝟐−𝟏𝟏𝒙+𝟕

Distribute the 2Distribute the -3

Combine Like Terms

Write in Descending Order

Multiplying Polynomials

(2 𝑥−3 )(𝑥+4)

3

𝟐 𝒙𝟐+𝟖 𝒙−𝟑 𝒙−𝟏𝟐

𝟐 𝒙𝟐+𝟓 𝒙−𝟏𝟐

FOILFirst: 2x2

Outer: + 8xInner: -3xLast: -12

Combine Like Terms

Write in Descending Order

(3 𝑥+1 )(2𝑥2+4 𝑥−5)

Multiplying Polynomials

4

𝟔 𝒙𝟑+𝟏𝟒 𝒙𝟐−𝟏𝟏𝒙−𝟓

Distribute orBox Method

Or Straight Up!

Combine Like Terms

Write in Descending Order

3x

+1

2x2 +4x -56x3 +12x2 -15x

+2x2 +4x -5

8 𝑥3+10 𝑥2−2 𝑥

5Factor Out the GCF

𝑮𝑪𝑭=𝟐 𝒙

Write in Descending Order if applicable

Prime Factor Each Term

Find the GCF

Factor out the GCFAnd write what remains

in the parenthesis

8x3 = 2 · 2 · 2 · x · x · x10x2 = 2 · 5 · x · x2x = 2 · x

𝟐 𝒙 (𝟒 𝒙¿¿𝟐+𝟓 𝒙−𝟏)¿

−21 𝑥5 𝑦 3−12𝑥3 𝑦2+15 𝑥2𝑦

6Factor Out the GCF

Write in Descending Order if applicable

Prime Factor Each Term

Find the GCF(First Term is negative so

GCF will be negative!)

Factor out the GCFAnd write what remains

in the parenthesis(Signs will change!)

21x5y3 = 3·7·x·x·x·x·x·y·y·y12x3y2 = 2·2·3·x·x·x·y·y 15x2y = 3·5·x·x·y

𝑮𝑪𝑭=−𝟑 𝒙𝟐 𝒚

−𝟑 𝒙𝟐 𝒚 (𝟕𝒙 ¿¿𝟑 𝒚 𝟐+𝟒 𝒙𝒚 −𝟓)¿

𝑥2−8𝑥+15

7Factoring Trinomials

Recognize what type of factoring it is

EASYHippo Butt

Product +15Sum -8

Both signs are –

-1 -15-3 -5

()()

(𝒙−𝟓)(𝒙−𝟑)

x x– 5 – 3

2 𝑥2+5 𝑥−12

8Factoring Trinomials

Recognize what type of factoring it is

Box Method orBottoms Up

Product -24Difference is +5

Signs are opposite +/-

-1 +24-2 + 12-3 +8-4 +6

(𝟐 𝒙−𝟑)(𝒙+𝟒)

2x

-3

x +4

2x2

+8x

-3x

-12

+8x

-3x

9 𝑥2−25

9Factoring Difference of Squares

Recognize what type of factoring it is

Difference of Squares!EASY

Hippo Butt

Perfect Square9x2 = 3x·3x

25 = 5·5

Opposite Signs

()()

(𝟑 𝒙−𝟓)(𝟑𝒙+𝟓)

3x 3x– 5 + 5

4 𝑥2+28𝑥+49

10Factoring Perfect Square Trinomials

Recognize what type of factoring it is

Perfect Square Trinomial!EASY

Hippo Butt

Perfect Square4x2 = 2x·2x

49 = 7·7

2x·7 = 14xDouble 14x = 28x

Same Signs! Both +

()()

¿

2x 2x+ 7 + 7

6 𝑥3+9 𝑥2−4 𝑥−6

11Factor by Grouping

(𝟐 𝒙+𝟑)(𝟑 𝒙𝟐−𝟐)

Recognize what type of factoring it is (4 Terms)

GROUP!Factor out GCF

If first term is negative,Factor out a negative

MUST be left with the same factors for each!

3 𝑥2(2𝑥+3)−2 (2𝑥+3)

NOTICE!

6 𝑥3 𝑦−12𝑥2 𝑦−48𝑥𝑦

12Factor Completely

First: Look for any GCF

Factor Out GCF

Keep factoring until there is nothing left to factor!

Recognize what type of factoring you are left with

EASYHippo Butt

𝑮𝑪𝑭=𝟔 𝒙𝒚

𝟔 𝒙𝒚 (𝒙𝟐−𝟐 𝒙−𝟖) +1 -8+2 -4

𝟔 𝒙𝒚 (𝒙−𝟒)(𝒙+𝟐)

13Factor Completely

First: Look for any GCF

Recognize 4 TermsGROUP!

Look at the factorsYou still have an x2

Difference of Squares!

(𝒙−𝟑)(𝒙𝟐−𝟒)

𝑥2(𝑥−3) −4 (𝑥−3)

NOTICE!

(𝒙−𝟑)(𝒙+𝟐)(𝒙−𝟐)

60 𝑥3+5 𝑥2−5 𝑥

14Factor Completely

First: Look for any GCF

Factor Out GCF

Keep factoring until there is nothing left to factor!

Recognize what type of factoring you are left with

Box Method/Bottoms Up

Don’t forget about GCF!

𝑮𝑪𝑭=𝟓 𝒙

𝟓 𝒙 (𝟏𝟐𝒙𝟐+𝒙−𝟏)

𝟓 𝒙 ()()

NEXT PAGE

60 𝑥3+5 𝑥2−5 𝑥

14Factor Completely

𝟓 𝒙 (𝟏𝟐𝒙𝟐+𝒙−𝟏)

𝟓 𝒙 ()()

4x

-1

3x +1

12x2

-1

+4x

-3x

Factor of -12

-1 +12-2 +6-3 +4

𝟓 𝒙 (𝟒 𝒙−𝟏)(𝟑 𝒙+𝟏)

Next Class:

Review Assignment Due!

Polynomial Unit TEST!TEST

20 Multiple Choice Polynomial Vocabulary Add/Subtract/Multiply Polynomials Factoring

8 Short Answer Factoring