How to factor polynomials

Introduction

Polynomials can be factored in many different ways. Today I will explain the different concepts.

Task

Concepts you will learn include Greatest Common Factor and difference of squares. But first, how do you Factor Polynomials?

As you travel through this WebQuest, you will gain a better understanding of what a polynomial is and with that understanding, you will be able to factor polynomials into the products using the different factoring techniques.

Process

How to factor a polynomial:

Step 1)First find two number that multiplies to get you c and add to get you b (x^2 + bx + c)

Example: x^2 + 6x + 8

( 8 = 4 x 2 and 4 + 2 = 6 )

Step 2) After you find the two numbers because the a is one the two numbers are your factors

Example: (x + 4) (x + 2)

How to factor a polynomial when x isn’t 1:

Step 1) first you multiply a and c to the number you factor

Example: 2x^2 + x - 3

2 x -3 = -6

-6 = -2 x 3 and -2 + 3 = 1

Step 2) Then use the box method with the 2 numbers

Example:

2x^2	-2x
3x	-3

Step 3) use the numbers you factor out as you factors

Example: ( 2x + 3 ) ( x - 1 )

How to factor with GCF:

Step 1) find the GCF

example: 3x^2 + 6x + 9

(in this example all of the terms are multiples of 3)

Step 2) Factor out the GCF

Example: 3 (x^2 + 2x + 3)

(this pulls out the 3 and leaves the number it was multiplied by)

How to factor with difference of squares:

Step 1) find out if these are perfect squares

Example: x^2 - 16

(these both are perfect squares)

Step 2) factor out the perfect squares

Example: x^2 - 16 = (x-4)^2

Step 3) Expand

Example: (x-4)(x+4)

Evaluation

Now it's your turn use the techniques learned to solve some problems. Each problem correct is a point and the person with the highest amount of points wins!

Problems: