1. 7.6
Factoring ax2 + bx + c
Students will be able to factor ax2 + bx + c.
This will be very similar to So if you did not get 7.5 you will have a difficult time here on out in this chapter until you get 7.5.
What can I say, math builds on itself!

2. Students will be able to factor ax2 + bx + c.
First a review of 7.5.

3. 1. Start with factoring out a GCF.
What is the GCF here. 5
Now it is like 7.5.
2. Start with the set up.
Don’t forget the GCF.
3. Look at the factors of the constant term. O
4. Take the factors of the constant term and put them in.
What is the constant term here. I
and
What are the factors of 2?
Check them by adding them because 2 is positive, the constant term.
5. Now you have to check your OI’s, the outer terms and inner terms.

4. 6. Now we have to put in the signs, + and/or -
+ because 2 is positive, the middle term
Now that was an easy one because it was just like 7.5 with factoring out a GCF.

5. 1. Start with factoring out a GCF.
Is there a GCF here? No
2.Now we have to consider the factors of the leading coefficient.
2.Now we have to consider the factors of the leading coefficient.
What is the leading coefficient here? 3
What are the factors of 3?
3 and 1
Since it is prime that makes it easier with the set up
3. Look at the factors of the constant term.
4. Take the factors of the constant term and put them in.
But now we have multiple possibilities. O
What is the constant term here. I
Check them by adding them because 2 is positive, the constant term.
and or
What are the factors of 2? O
5. Now you have to check your OI’s, the outer terms and inner terms.
So which one do we want? I
and

6. 6. Now we have to put in the signs, + and/or -
- because 7 is negative, the middle term

7. We would have more possibilities!!
So the steps are the same as 7.5, the last section,
except now we have to deal with the leading coefficient in our 1st step
And that creates multiple possibilities for the placement of the factors of the constant term.
What would happen if our leading coefficient had more factors?
We would have more possibilities!!
So let’s try another one!!

8. 1. Start with factoring out a GCF.
Is there a GCF here? No
2.Now we have to consider the factors of the leading coefficient.
2.Now we have to consider the factors of the leading coefficient.
What is the leading coefficient here? 4
What are the factors of 4?
4 and 1
2 and 2
3. Look at the factors of the constant term.
4. Take the factors of the constant term and put them in.
But now we have multiple possibilities. O
What is the constant term here. I
Check them by adding them because 3 is positive, the constant term.
and or
What are the factors of 3? O
5. Now you have to check your OI’s, the outer terms and inner terms.
So which one do we want?
Do we even need to check I
and

9. 6. Now we have to put in the signs, + and/or -
+ because 13 is positive, the middle term

10. 1. Start with factoring out a GCF.
Is there a GCF here? No
2.Now we have to consider the factors of the leading coefficient.
What is the leading coefficient here? 2
What are the factors of 2?
2 and 1
2.Now we have to consider the factors of the leading coefficient.
3. Look at the factors of the constant term.
4. Take the factors of the constant term and put them in.
But now we have multiple possibilities. O
What is the constant term here. I
Check them by subtracting them because 7 is negative, the constant term.
and or
What are the factors of 7? O
5. Now you have to check your OI’s, the outer terms and inner terms.
So which one do we want? I
and

11. And that is our middle term, those are the signs we want.
6. Now we have to put in the signs, + and/or -
Since our OI’s gave us
And that is our middle term, those are the signs we want.
How do we get a +2x
How do we get a -7x
How do we check?

12. Is there a GCF here?
Yes -1
1. Start with factoring out a GCF.
2.Now we have to consider the factors of the leading coefficient.
4 and 1
2 and 2
3. Look at the factors of the constant term. O
What is the constant term here.
What are the factors of 5?

13. Check them by subtracting them because 5 is negative, the constant term.
4. Take the factors of the constant term and put them in.
Can we stop?
5. Now you have to check your OI’s, the outer terms and inner terms.
So which one do we want?
Are these different?
NO!
Do we need them both? No.

14. That is NOT our middle term, those are NOT the signs we want.
6. Now we have to put in the signs, + and/or -
Since our OI’s gave us
That is NOT our middle term, those are NOT the signs we want.
So what if we change the order of subtraction?
Now we have the sign we need!!
How do we get a +10x
How do we get a -2x

15. You Try!!!
Factor.
Check them by adding them because 8 is positive, the constant term.
Start with factoring out a GCF.
There is none so skip to next step
5. Now you have to check your OI’s, the outer terms and inner terms.
2.Now we have to consider the factors of the leading coefficient.
3 and 1
4. Take the factors of the constant term and put them in.
1 and 8
2 and 4
3. Look at the factors of the constant term.
1 and 8
2 and 4
Can we stop?
Do we have to keep going?
So which one do we want?

16. You Try!!!
Factor.
6. Now we have to put in the signs, + and/or -
We are adding the OI’s because 8 is positive
we need to have the same signs,
And that is the sign of the middle term
So they are both – (minus)

17. Last one
But First
Let us review what we learned today
Students will be able to factor ax2 + bx + c.

18. Last one
Factor.
But we want a negative 19x
So switch the order of subtraction
Do we need this one?
Good Job!