Download Chapter 5 – Quadratic Functions and Factoring

Chapter 5 – Quadratic
Functions and Factoring
5.3 – Factoring x2 + bx + c
5.3 – Factoring x2 + bx + c
Today we will be learning how to:
Factor trinomials of the form x2 + bx + c
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!!
5.3 – Factoring x2 + bx + c
Example 1
Factor out the GCF of:
8y2 + 16y5
6a4 – 8a2 + 2a
5.3 – Factoring x2 + bx + c
Example 2
Factor out the GCF of:
-15x3y + 9x2y7
-5x2y – x2 + 3x3y5 + 11x7
5.3 – Factoring x2 + bx + c
HOMEWORK
5.3 Part 1 Practice
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)
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
c
2
x
+ bx + c
multiply
b
add
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
5.3 – Factoring x2 + bx + c
Example: Factor r2 + 4r + 3
(r
)(r
)
3
4
multiply
add
5.3 – Factoring x2 + bx + c
Example 1
Factor the expression.
x2 + 10x + 9
x2 + 8x + 15
5.3 – Factoring x2 + bx + c
Example 2
Factor the expression.
x2 – 10x + 25
x2 – 2x + 1
5.3 – Factoring x2 + bx + c
Example 3
Factor the expression.
x2 – 14x + 24
x2 + 6x + 9
5.3 – Factoring x2 + bx + c
HOMEWORK
5.3 Part 2 Practice Worksheet
5.3 – Factoring x2 + bx + c
HOMEWORK
5.3 Practice A
#2 – 4, 6 – 8, 11 – 12, 15, 18
5.3 – Factoring x2 + bx + c
Example 1
Factor the expression.
x2 – 3x – 18
x2 + 5x – 6
5.3 – Factoring x2 + bx + c
Example 2
Factor the expression.
x2 – 2x – 35
x2 + 4x – 21
5.3 – Factoring x2 + bx + c
Example 3
Factor the expression.
x2 + x – 20
x2 – 4x – 5
5.3 – Factoring x2 + bx + c
HOMEWORK
5.3 Part 3 Practice
5.3 – Factoring x2 + bx + c
HOMEWORK
5.3 Practice B Worksheet
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