10/6/11 5.5 Factoring Trinomials
•  Recognize and factor perfect square trinomials.
•  Factor trinomials of the form x2+bx+c and ax2+bx+c.
•  Factor trinomials of the form ax2+bx+c by grouping.
•  Factor polynomials completely.
Example
•  Solve the following equation:
(x-2)(x+3)=0
1 10/6/11 (x-2)(x+3)=0
•  What if instead I was given:
•  Solve:
x2 +x -6 = 0
•  Factoring polynomials is a process opposite to multiplying
them. But both are really just an instance of
DISTRIBUTIVE PROPERTY
Factor :
8x 3 −4x2
3s2t−6st2 +3t 3
€
2 10/6/11 Factor :
2y(y + 5) − 3(y + 5)
y 2 − 3y + 4 y −12
€
More examples
z 3 + 2z 2 − 4z − 8
(x − 3) 2 − 9
y3 + 8
81z 2 − 25
€
3 10/6/11 x2
3
4x
x2
x2
x x x x
1
1
1
x
xxx
1
1
1
Factoring trinomials
x 2 + 3x + 2
x 2 − 5x + 6
€
4 10/6/11 Factoring
We need to find two numbers whose
product is c and whose sum is b.
Little different
2z 2 + 4z − 6
€
5 10/6/11 Little different
3y 2 − y − 30
€
Factoring
6 10/6/11 5.6 Solving Polynomial Equations by
Factoring.
•  Use the Zero-Factor Property to solve equations.
•  Solve quadratic equations by factoring.
•  Solve higher-degree polynomial equations by factoring.
Quadratic equations
are equations that can be written in the form
where a ≠ 0.
7 10/6/11 Solving quadratic equations
•  Strategy #1: FACTOR
•  Examples:
Solving quadratic equations
•  Strategy #1: FACTOR
•  Examples:
8 10/6/11 Solving quadratic equations
•  Strategy #1: FACTOR
•  Examples:
Solve the equations
9 10/6/11 Solve the equations
Solve the equations
10 10/6/11 One more
Word problem
•  The outside dimensions of a picture frame are 28
centimeters and 20 centimeters. The area of the exposed
part of the picture is 468 square centimeters. Find the
width w of the picture frame.
11 10/6/11 Garden Problem revisited…
I want to put a fence around my garden to keep the dogs
out. To make it easy on myself I’ll make it rectangular. I
bought 60 yards of lattice fence, and I want to use all of
it. And, I want the yard to have area of 250 square yard.
Can it be done?
12