1. Chapter 5 – Quadratic Functions and Factoring
5.3 – Factoring x2 + bx + c

2. 5.3 – Factoring x2 + bx + c Today we will be learning how to:
Factor trinomials of the form x2 + bx + c

3. 5.3 – Factoring x2 + bx + c
If all terms of a polynomial have a factor(s) in common, you can factor out that greatest common factor (GCF)
When factoring, ALWAYS CHECK FOR A GCF FIRST!!

4. 5.3 – Factoring x2 + bx + c Example 1 Factor out the GCF of:
8y2 + 16y5
6a4 – 8a2 + 2a

5. 5.3 – Factoring x2 + bx + c Example 2 Factor out the GCF of:
-15x3y + 9x2y7
-5x2y – x2 + 3x3y5 + 11x7

6. HOMEWORK 5.3 Part 1 Practice
5.3 – Factoring x2 + bx + c
HOMEWORK 5.3 Part 1 Practice

7. 5.3 – Factoring x2 + bx + c
We know how to write (x + 3)(x + 5) as x2 + 8x + 15
Now we’re going to learn how to take a trinomial like x2 + 8x + 15 and write it as a product of binomials (x + 3)(x + 5)

8. 5.3 – Factoring x2 + bx + c Factoring Polynomial When…
The degree is 2 (quadratic)
The number of terms is 3 (trinomial)
The coefficient of the squared term is 1
x2 + bx + c b
add c
multiply

9. 5.3 – Factoring x2 + bx + c Steps to factoring success
Draw your parentheses and fill in the variable.
In your x-puzzle: b goes in the addition spot and c goes in the multiplication spot.
What will your signs need to be?
Solve the x-puzzle and put your answer in ( )
Check your work by distributing

10. 5.3 – Factoring x2 + bx + c Example: Factor r2 + 4r + 3 (r )(r ) 4 3
multiply
add

11. 5.3 – Factoring x2 + bx + c Example 1 Factor the expression.
x2 + 10x + 9
x2 + 8x + 15

12. 5.3 – Factoring x2 + bx + c Example 2 Factor the expression.
x2 – 10x + 25
x2 – 2x + 1

13. 5.3 – Factoring x2 + bx + c Example 3 Factor the expression.
x2 – 14x + 24
x2 + 6x + 9

14. 5.3 Part 2 Practice Worksheet
5.3 – Factoring x2 + bx + c
HOMEWORK
5.3 Part 2 Practice Worksheet

15. 5.3 – Factoring x2 + bx + c HOMEWORK 5.3 Practice A
#2 – 4, 6 – 8, 11 – 12, 15, 18

16. 5.3 – Factoring x2 + bx + c Example 1 Factor the expression.
x2 – 3x – 18
x2 + 5x – 6

17. 5.3 – Factoring x2 + bx + c Example 2 Factor the expression.
x2 – 2x – 35
x2 + 4x – 21

18. 5.3 – Factoring x2 + bx + c Example 3 Factor the expression.
x2 + x – 20
x2 – 4x – 5

19. 5.3 – Factoring x2 + bx + c
HOMEWORK
5.3 Part 3 Practice

20. 5.3 – Factoring x2 + bx + c
HOMEWORK
5.3 Practice B Worksheet
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