1. 4.3 Solving Quadratic Equations by Factoring

2. (x + 3)(x + 5) = + 5x +3x +15 (x + 3)(x + 5)
Recall multiplying these binomials to get the standard form for the equation of a quadratic function:
(x + 3)(x + 5) =
+ 5x
+3x
+15
The “reverse” of this process is called factoring. Writing a trinomial as a product of two binomials is called factoring.
(x + 3)(x + 5)

3. Factor
Since the lead coefficient is 1, we need two numbers that multiply to –28 and add to –12.
Factors of -28
-1,28
1,-28
-2,14
2,-14
-4,7
4,-7
Sum of Factors 27
-27 12
-12 3 -3
Therefore:

4. Factor the expression:
= (x-3)(x+7)
Cannot be factored

5. Factoring a Trinomial when the lead coefficient is not 1.
We need a combination of factors of 3 and 10 that will give a middle term of –17. Our approach will guess and check. Here are some possible factorizations:
This is the factorization we seek.

6. Special Factoring Patterns you should remember:
Pattern Name Pattern Example
Difference of Two Squares
Perfect Square Trinomial

7. Factor the quadratic expression:

8. A monomial is an expression that has only one term
A monomial is an expression that has only one term. As a first step to factoring, you should check to see whether the terms have a common monomial factor.
Factor:

9. You can use factoring to solve certain quadratic equation
You can use factoring to solve certain quadratic equation. A quadratic equation in one variable can be written in the form
where
This is called the standard form of the equation:
If this equation can be factored then we can use this zero product property.
Zero Product Property
Let A and B be real number or algebraic expressions. If AB = 0 the either A=0 or B=0

10. Solve:
So, either (x+6)=0
x = -6
Or (x – 3)=0
x = 3
The solutions are –6 and 3.
These solutions are also called zeros of the function
Notice the zeros are the x-intercepts of the graph of the function.