Module 10: Lesson 5: Factoring Polynomials

Module 10: Lesson 5: Factoring Polynomials

By Mr. Carozza and Ms. San

Last topic of the school year!!!

In order to be successful with this, we must know our factors.

Factors are all the numbers that can multiply to equal the original number.

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ex: Factors of 20 --> 1​*20, 2*10, 4*5 so, 1, 2, 4, 5, 10, 20 are factors of 20

Use your calculator if you are forgetting your times tables

Open Ended

What are the factors of 24?

Multiple Choice

Which number is NOT a factor of 24?

• 2

• 12

• 14

• 8

Open Ended

What are the factors of 36?

Multiple Choice

Which number is NOT a factor of 36?

• 1

• 4

• 6

• 13

Open Ended

What are the factors of 15?

Multiple Choice

What are ALL the factors of 15?

• 1, 3, 5, 15

• 1, 15

• 1, 3, 5, 7, 15

• 2, 4, 6, 8

Let's apply this to Polynomials

We will start with a trinomial, and factor to change it to two binomials.

The generic form of trinomials is

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ax² + bx + c

Let's first be able to identify our a, b, c values given a trinomial.

a = ______

​

b = ______

​

c = ______​

x² + 7x - 10

a = ______

​

b = ______

​

c = ______​

x² - 5x + 12

Multiple Choice

What is a, b, c for the following trinomial?

$$x^2+x-6$$  

• a = 2

  b = 1

  c = 6

• a = 1

  b = 1

  c = 6

• a = 1

  b = 1

  c = -6

• a = 1

  b = 0

  c = -6

Let's go through the Steps

​Step 1: Identify a, b, c

a = ______

​

b = ______

​

c = ______​

​Step 2: Set up your blank lines

​

______ * ______ = a * c​

​

______ + ______ = b​

​

​

Subject | Subject

Step 3: Parenthesize your answer

​Put your answers into parantheses with the variable at the beginning of each ( )

​

( x ) ( x )

​Complete this on the next slide.

a = ______

​

b = ______

​

c = ______​

​Identify a, b, c

Let's try an example: x² + 8x + 12​

Some text here about the topic of discussion

Multiple Choice

What is a, b, c for the trinomial

$$x^2+8x+12$$  

• a = 1

  b = 8

  c = 12

• a = 0

  b = 8

  c = 12

• a = 1

  b = 8

  c = -12

​Set up your blank lines

​

______ * ______ = a * c

​

______ * ______ = b​

​

Subject | Subject

Multiple Choice

What is the proper setup for the trinomial

$$x^2+8x+12$$  

• -6 * 2 = 12

  -6 + 2 = 8

• 6 * -2 = 12

  6 + -2 = 8

• 6 * 2 = 12

  6 + 2 = 8

• -6 * 2 = 12

  6 + -2 = 8

Parenthesize your answer

​Simply put your answers into parentheses with the variable at the start of each ( )

​

( x ) ( x )

​

ex: (x + 5) ( x + 3)​

Multiple Choice

What is the final factor to the trinomial

$$x^2+8x+12$$  

• $$\left(x+6\right)\left(x-2\right)$$  

• $$\left(x-6\right)\left(x-2\right)$$

• $$\left(x-6\right)\left(x+2\right)$$

• $$\left(x+6\right)\left(x+2\right)$$

Multiple Choice

Factor: $$x^2-3x-18$$  

• $$\left(x+6\right)\left(x+3\right)$$  

• $$\left(x-6\right)\left(x+3\right)$$

• $$\left(x-6\right)\left(x-3\right)$$

• $$\left(x-9\right)\left(x+2\right)$$

There are 4 Practice problems on the guided notes.

​Please finish the last 4 Practice problems on your own.

You are great