__ARC Video Library__

How to Factor Polynomials

Presented by UMO SI leader Kylie Ward, this video explains how to Factor Polynomials which is a key concept in MAT 120.

MAT 120 Factoring Polynomials |

## Video Script

- This video is brought to you by the UMO Academic Resource Center.
- My name is Kylie Ward and this video tutorial will cover factoring polynomials for MAT 120.
- Factors
- When an integer is written as a product of integers, each of the integers in the product is a factor of the original number
- Factoring is writing a polynomial as a product of polynomials

- Helping with factoring is knowing how to find the Greatest Common Factor, otherwise known as GCF.
- Greatest common facts is the largest quantity that is a factor of all the integers or polynomials involved
- To find the GCF of a list of integers, you can:
- Use a prime factorization method: factor tree or listing method
- Identify the commons prime factors of both integers or terms
- Then take the product of all common prime factors
- Remember if there are no common factors, the GCF is 1

- Examples of GCF
- 6x^5 and 4x^3
- List the factors of both
- 6x^5=2*3*x*x*x*x*x
- 4x^3=2*2*x*x*x

- So the GCF is what both have in common = 2x^3

- 6x^5 and 4x^3
- Another example that is easier is:
- 12 and 8, again you list the factors
- 12=2*2*3
- 8=2*2*2

- GCF=2*2= 4

- 12 and 8, again you list the factors
- Now that we know the GCF of 2 terms, we can factor polynomials
- 1st step is to find the GCF, which we previously just learned
- Then write the polynomial as a product by factoring out the GCF from all terms
- Remaining factors will form a polynomial

- Examples of factoring out the GCF of polynomials
- 6x^3-9x^2+12x
- List factors for each individual term
- Then see what is the same for all 3

- Since all factor out a 3 and x that is what you place on the outside of the parenthesis
- Then you keep what is left over in parenthesis
- This is where 2x^2 -3x +4 comes from

- 6x^3-9x^2+12x
- Another example is 6(x+2) –y(x+2)
- The GCF is (x+2)
- Then you have 6-y left over so you combine these terms together with the final answer being (x+2)(6-y)

- Remember that factoring out the GCF from the terms of a polynomial should be the 1st step
- Now a for a harder example, factor 90+15y^2 -18x -3xy^2
- The only thing common between all these terms is that you can pull out a 3
- So, on the inside you are left with 30 + 5y^2 -6x –xy^2
- Then you can factor the inside by splitting the 4 terms up by 30 and 5y^2 and -6x and –xy^2
- GCF of 30 and 5y^2 is 5 left with 6+y^2
- GCF of -6x-xy^2 is –x so then you are left with 6+y^2

- When you end up left with the same thing for both terms, you can combine what you factored out by pulling down the 3 from being factored out earlier, writing what was common (6+y^2), and combing what you factored (5-x)

- Now a for a harder example, factor 90+15y^2 -18x -3xy^2
- This concludes the tutorial video, for more resources contact the UMO Academic Resource Center or e-mail us at arc@umo.edu. Thank you for listening.