1. Basic Factoring of Polynomials
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2. Solving Quadratic Polynomials
Three steps to solving quadratic polynomials
Solve by factoring
Solve by using the square root property
Solve by using the quadratic equation

3. Quadratic Polynomials
How does one isolate ‘x’ in a case like the following?
It is unnecessarily difficult.
Therefore, other methods must be used.

4. Quadratic factoring Example: First we need to…
MAKE THE EQUATION EQUAL TO ZERO
So:
This polynomial can be factored by considering the following:
The polynomial has three terms
First, Middle, and Last
z2 + 4z + 4
z2 + 4z + 4 = 0

5. Quadratic factoring (Cont.)
The first term is z2
The Middle term is 4z
The Last terms is 4
To factor, the best way to start is to place the parenthesis for factoring:
( F L ) ( F L )
The F * F must equal the first term.
The L * L must equal the last term.

6. Quadratic factoring (Cont.)
The inner plus the outer must equal the middle term.
z * z = z2  First Term
2z + 2z = 4z  Middle Term
2 * 2 = 4  Last Term

7. Quadratic factoring (Cont.)
In summary:
( F L ) ( F L )
F * F = First term
L * L = Last Term
Inner + Outer = Middle Term

8. Example Factor: x2 + x – 6 First: (x )(x ) Second: 3 * (-2) = -6
3x - 2x = x
Third:
Answer: (x + 3)(x - 2)

9. Quadratic Equation
A quadratic function can also be solved by the quadratic formula:
It must be in standard form:
Ax2 + Bx + C = 0

10. Cubic Polynomials
These polynomials can be solved by using the synthetic division or if possible, by factoring.
Only factoring will be considered

11. Some polynomials can be grouped to factor the like terms.
By Factoring
Some polynomials can be grouped to factor the like terms.
x3 + 2x2 + 2x + 4 = 0
Example:
First: Group the terms
(x3 + 2x2) + (2x + 4) = 0
Second: Factor out common terms
x2 (x + 2) + 2 (x + 2) = 0
Third: Factor the (x + 2) term
Answer: (x2 + 2)(x + 2) = 0

12. SUMMARY Polynomials can be of various degrees; the most popular are:
Linear
Quadratic
Cubic
Factoring is a tool to help solve for a variable.
In order to solve by factoring it is necessary to MAKE THE EQUATION EQUAL TO ZERO.

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Questions?

14. Links and Handouts Working with Polynomials Worksheet
Factoring Polynomials Handout
Completing the Square Handout
Algebra and Logarithmic Functions Handout
Polynomial Quiz
Working with Polynomials Quiz