1. 7.5 Factoring x2 + bx + c Students will be able to factor x2 + bx + c.
This is the easy factoring and you need to remember how to FOIL.
Review of FOILing.
First
Outer
Inner
Last
Combine the like terms which are from OI.

2. So Factoring is undoing FOILing.
1. Start with the set up.
This sets the first terms.
2. Look at the factors of the constant term. O
3. Take the factors of the constant term and put them in.
Now this starts to set the last terms.
What is the constant term here. I
and
What are the factors of 15?
Check them by adding them because 15 is positive, the constant term. O
4. Now you have to check your OI’s, the outer terms and inner terms. I
Now which one matches the middle term of our problem?

3. So Factoring is undoing FOILing.
5. Now we have to put in the signs, + and/or -
+ because 8 is positive, the middle term

4. So, what were those steps again?
1. Start with the set up.
This sets the first terms.
The F in FOIL.
2. Look at the factors of the constant term.
3. Take the factors of the constant term and put them in.
Now this starts to set the last terms.
The L in FOIL.
4. Now you have to check your OI’s, the outer terms and inner terms.
5. Then we have to put in the signs, + and/or -

5. So let us try another one together.
1. Start with the set up.
This sets the first terms.
2. Look at the factors of the constant term. O
3. Take the factors of the constant term and put them in.
Now this starts to set the last terms.
What is the constant term here. I
and
What are the factors of 16?
Check them by adding them because 16 is positive, the constant term. O
4. Now you have to check your OI’s, the outer terms and inner terms. I
If we have one that matches the middle term of our problem we can stop.

6. So let us try another one together.
5. Now we have to put in the signs, + and/or -
+ because 10 is positive, the middle term
Of course we can always check our working by FOILing.
Now what if the middle term were a -10?
Everything is the same except the sign of the middle term.
They are - because the middle term is -.

7. You Try!!!
Factor.
1. Start with the set up.
This sets the first terms.
2. Look at the factors of the constant term.
3. Take the factors of the constant term and put them in.
Now this starts to set the last terms.
What is the constant term here.
What are the factors of 24?
4. Now you have to check your OI’s, the outer terms and inner terms.
Which one matches the middle term of our problem?

8. You Try!!!
5. Now we have to put in the signs, + and/or -
- because 14 is negative, the middle term

9. Now what if the constant term is negative.
1. Start with the set up.
This sets the first terms.
2. Look at the factors of the constant term. O
3. Take the factors of the constant term and put them in.
Now this starts to set the last terms.
Check them by SUBTRACTING them because 21 is negative, the constant term.
What is the constant term here. I
and
What are the factors of 21? O
4. Now you have to check your OI’s, the outer terms and inner terms. I
Now which one matches the middle term of our problem?

10. Now what if the constant term is negative.
5. Now we have to put in the signs, + and/or -
the bigger factor must have the sign of the middle term.
the signs must be opposite because we are subtracting because the constant term is negative.
Of course we can always check our working by FOILing.
First
Outer
Inner
Last

11. You Try!!!
Factor.
1. Start with the set up.
This sets the first terms.
2. Look at the factors of the constant term.
3. Take the factors of the constant term and put them in.
Now this starts to set the last terms.
REMEMBER:
Check them by SUBTRACTING them because 42 is negative, the constant term.
What is the constant term here.
What are the factors of 42?
4. Now you have to check your OI’s, the outer terms and inner terms.
Which one matches the middle term of our problem?

12. You Try!!!
5. Now we have to put in the signs, + and/or -
the bigger factor must have the sign of the middle term.
the signs must be opposite because we are subtracting because the constant term is negative.
Of course we can always check our working by FOILing.
First
Outer
Inner
Last

13. Last two
But First
Let us review what we learned today
Students will be able to factor x2 + bx + c.

14. Last two
Factor.
Good Job!