Factoring Day 1

Factoring Day 1

When the factors are integers

First, let's review Zeros.....

with some practice....

Multiple Choice

True or false:
The solutions, roots, x-intercepts, and zeros of a quadratic equation are all the same thing.

• True
• False, because the solution and root are the same but the x-intercept and zero are different
• False, because the x-intercept and root are the same but the zero and solution are different
• False, they are all different

Multiple Choice

Find the zeros of the function above.

*remember to change n to x in Desmos*

• -4, 2

• -2, 4

• -16

• -4

Multiple Choice

What are the zeros of the quadratic function?
y = x² - 2x - 15

• x = -2
  x = -15
• x = -3
  x = 5
• x = 3
  x = -5
• x = 1
  x = -16

Multiple Choice

Find the roots/zeros of x² + x - 2

• -1, 2
• -2, 1

How do I find the Factors of a Quadratic?

• Graph the Quadratic in Desmos and find the Zeros

• Plot the Zeros on a number line

• Answer the question: How do I get back to zero from here? HINT: Do I add or subtract?

• Write out my factors

• Check to see if there is a GCF by graphing my answer in Desmos

Let's look at this example..

• What are the zeros of this graph?

Fill in the Blanks

What are the zeros of this graph?

Here is the number line with the zeros plotted.

How do we get back to zero from -5?

HINT: Do we add or subtract?

How do we get back to zero from 8?

HINT: Do we add or subtract?

Fill in the Blanks

If you are at -5 on a number line, would you add or subtract to get back to zero?

Fill in the Blanks

If you are at 8 on a number line, would you add or subtract to get back to zero?

Next....

Now we can write our factors

Check our answer in Desmos

Do the graphs match? (Overlap)

Poll

Does this make sense?

• Ummmm no?????

• I think so.....

• Wow this is cool. I get it!

• More practice needed

Let's look at another example..

• What are the zeros of this graph?

Here is the number line with the zeros plotted.

How do we get back to zero from -4?

HINT: Do we add or subtract?

How do we get back to zero from 5?

HINT: Do we add or subtract?

Fill in the Blanks

If you are at -4 on a number line, would you add or subtract to get back to zero?

Fill in the Blanks

If you are at 5 on a number line, would you add or subtract to get back to zero?

Next....

Now we can write our factors

Check our answer in Desmos

Do the graphs match? (Overlap)

One last Example

Super important

Let's start by graphing

 $3x^2+9x-30$  

Here is the number line with the zeros plotted.

How do we get back to zero from -5?

HINT: Do we add or subtract?

How do we get back to zero from 2?

HINT: Do we add or subtract?

Fill in the Blanks

If you are at -5 on a number line, would you add or subtract to get back to zero?

Fill in the Blanks

If you are at 2 on a number line, would you add or subtract to get back to zero?

Next....

Now we can write our factors

Let's Check our answer....

This does not look right. Our graphs don't overlap. Now what?

Our graphs don't match because we need to find what is called a Greatest Common Factor or GCF

• Let's look at the original quadratic:

   $3x^2+9x-30$  

• We know we have to find a number that goes into all these numbers evenly.

Fill in the Blanks

What is the largest number that goes into 3, 9 and -30 evenly?

Now we head to Desmos with our GCF

We type the GCF in front of our original answer and see if it matches.

That's all there is to it

Let's Practice

Multiple Choice

Factor the trinomial.

• (x+27)(x+1)

• (x+9)(x+3)

• (x+28)(x+1)

• (x+14)(x+13)

Multiple Choice

Let's factor this one:  $2x^2-14x+12$  

•  $\left(x-6\right)\left(x-1\right)$  

•  $\left(x+1\right)\left(x+1\right)$  

•  $2\left(x-1\right)\left(x-6\right)$  

•  $2\left(x+1\right)\left(x+6\right)$  

Multiple Choice

Factor the trinomial.

• (x+5)(x+4)

• (x+10)(x+2)

• (x+20)(x+1)

• (x+4)(x+3)