Unit 4 L1

Unit 4 Lesson 1 and 2
Reviewing Factoring

In this lesson, you will review X-factoring and GCF factoring. There are videos you should watch throughout! ​
Look at the nice cherry blossoms ----->

Find the largest exponent!

And look at these animals? Which is your favorite?
I think I like the fox best :)

​​Degree

​First, look at your degree. If it is an even number, end behavior is either up up or down down. If the front number is negative, down down. If the front is positive, up up.

​​End Behavior

First, look at your degree. If it is an odd number, end behavior is either down up or up down. If the front number is negative, up down. If the front is positive, down up.

​​End Behavior

Multiple Choice

State the degree and end behavior of this function:

$$3x^2+2x-8$$

Write the answers on your paper too!

• Degree 2

  End Behavior

  Up Up

• Degree 3

  End Behavior

  Up Up

• Degree 2

  End Behavior

  Down Down

Multiple Choice

State the degree and end behavior for this function

$$x^2-12x+36$$

• Degree 2

  End Behavior Up up

• Degree 2

  End Behavior Down up

Categorize

Options (5)

$$3x^2+75$$  

$$25x^2-50x$$  

$$x^2-7x+18$$  

$$x^3+2x^2+7x+14$$  

$$2x^4+10x^3+12x^2$$  

Organize these options into the right categories

Degree 2

Degree 3

Degree 4

Categorize

Options (5)

$$3x^2+75$$  

$$25x^2-50x$$  

$$2x^4+10x^3+12x^2$$  

$$x^2-7x+18$$  

$$x^3+2x^2+7x+14$$  

Organize these options into the right categories

Up Up End Behavior

Down Up End Behavior

Let's Review GCF

​Greatest Common Factor

This could be a number that all terms can be divided by.
It could also be a variable, like x because all terms include that variable.
When we factor with GCF, we divide all terms by the GCF.
Numbers divide numbers. X reduces the exponent.

3x²+75

Method: GCF

Factored expression: 3(x²+25)

No x-intercepts. This is a concave up parabola shifted up 25 units. There are no x-intercepts so we have 2 imaginary solutions.

Multiple Choice

What is the GCF for $$25x^2-50x$$ ?

Hint: this can be re-written as

$$25\cdot x\cdot x-25\cdot2\cdot x$$

• GCF= 25x

  Factored Form:

  $$25x\left(x-2\right)$$

• GCF is 25

  Factored Form:

  $$25\left(x^2-2x\right)$$

25x²-50x

​Method: GCF

Factored form: 25x (x-2)

This has two factors of x so it has 2 x-intercepts. We can find them with algebra by switching sign of the factors or by graphing and finding x intercepts.
Location: x=0 and x=2 No imaginary zeros

Multiple Choice

What is the GCF of

$$x^2-12x+36$$

• GCF=2

• GCF=6

• no GCF

Not every expression has a GCF! We need another method.

​X-Factoring!

1. You should have a quadratic expression (degree 2).

2. Identify a, b, and c.

3. Multiply a *c.

4. Find all the factors of this value.

5. Choose the one factor pair that add/subtract to give you b value.

x²+7x+12

​This is quadratic with no GCF. Lets x-factor.

a=1 b=7 c=12
a*c= 12
Factors of 12: 1*12 or 2*6 or 3*4

Which factors add to be 7? 3 and 4!
Factored expression: (x+3)(x+4) Location of x-intercepts x=-3 and x=-4

Multiple Choice

Factor

$$x^2-12x+36$$

• (x+6)(x+6)

• (x-6)(x-6)

• (x+6)(x-6)

x²-12x+36

​This is quadratic with no GCF. Lets x-factor.

a=1 b=-12 c=36
a*c= 36
Factors of 12: 1*36 or 2*18 or 3*12 or 4*9 or 6*6

Which factors add to be 12? -6 and -6
Factored expression: (x-6)(x-6) Location of x-intercepts x=6 with multiplicity. No imaginary zeros!

x²-7x+18

​This is quadratic with no GCF. Lets x-factor.

a=1 b=-7 c=18
a*c= 18
Factors of 12: 1*18 or 2*9 or 3*6

Which factors add (or subtract) to be -7?

Multiple Choice

Factor

$$x^2-7x+18$$

• (x+2)(x+9)

• (x+2)(x-9)

• (x+9)(x-2)

Multiple Choice

Factor:

$$2x^4+10x^3+12x^2$$

Hint: First find GCF. Then X factor.

• $$2x^2\left(x+3\right)\left(x+2\right)$$

• $$2x^2\left(x+5\right)\left(x+1\right)$$

You should have several rows completed.

​Row 1 and Row 4 are both blank. We will discuss in class.

Now consider what equivalent means. How do we prove equivalence? With algebra we can factor or multiply. With a graph, what can we look for?
Answer the question on the bottom of your paper!