Polynomial Functions (Factoring and Long Division)

Hi it's Albien.
So today we learned about factoring using the GCF (Greatest Common Factor). The GCF of two or more monomials is the greatest common factor that divide each of the monomials.

Example 1:

Factoring by Grouping
In some cases there is no GCF for ALL the terms in a polynomial. If you have four terms with no GCF, then try factoring by grouping.

Step 1: Group the first two terms together and then the last two terms together.

Step 2: Factor out a GCF from each separate binomial.

Step 3: Factor out the common binomial.

Example 2:

Factoring the Difference of Two Squares
(ax)² - b² = (ax + b) (ax - b)
















Factoring Difference of Cubes
Used for binomials that are a difference of two perfect cubes.
x³ - y³ = (x - y) (x² + xy + y²)

 Factoring Sum of Cubes
 Used for binomials that are a sum of two perfect cubes.
x³ + y³ = (x + y) (x² - xy + y²)
















Factoring Perfect Square Trinomials
x² + 2xy + y² = (x + y)²
x² - 2xy + y² = (x - y)²

Factoring Trinomials of the form x² + bx + c with leading coefficient 1
x² + bx + c = (x + u) (x + v), where u and v are integers that satisfy the following:
1.) uv = c
2.) u + v = b

Here are some hints for factoring a trinomial of the form x² + bx + c.
1.) If c is positive, then u and v have the same sign. They are both positive if b is positive. They are both negative if b is negative.
2.) If c is negative, then u and v have opposite signs.

Long Division

That's all. And don't forget that the Transformation Assignment #3 is due on Friday.

Have a wonderful day!