4.1 – Common Factors in Polynomials
Recall:

Standard Form of Quadratic Relation: ____________________________

Factored Form of Quadratic Relation: ____________________________

To convert from FACTORED FORM to STANDARD FORM, you ________________.
o
Example: y = (x – 3) (x + 4)
 To convert from STANDARD FORM to FACTORED FORM, you ________________.
 To FACTOR means to express an algebraic expression as the _____________ of two or more
terms.
 Factoring is the opposite of ___________________.
 Factoring involves _______________ whereas Expanding involves __________________.
GOAL: Factor algebraic expressions by dividing out the greatest common factor
 To factor an expression, you have to find the Greatest Common Factor (GCF).

The GCF is the ____________ number and/or variable that will divide evenly into all terms
of the expression.
Steps to Finding the GCF of a Set of Terms
Example: 3x, 6x2, 12x3
1.) Determine the largest coefficient that
divides evenly into each term.
2.) Determine the variable that exists in each
term.
3.) Determine the smallest degree that
appears on the variable that is found in
each term.
Example #1: State the greatest common factor of each set of terms.
a) 6x, 10y, 12z
b) 5x2, 12x5, 7x3
c) 4a, 12a3, 8a2
Steps for Factoring an Expression
Example: 4x2 + 6x4 – 12x3
1.) Find the _______ of the expression.
2.) Place the GCF ________________ of
a bracket.
3.) Divide every term of the original
equation by the GCF and place these
new terms ________________ the
bracket.
Example #2: Factor each expression.
a) 25a2 – 20a

b) x4 – x6 + x2
c) 3y4 – 9y2 + 15y3
In some cases, there may be more than one common variable, which you will place in a
bracket. You may need to “group” similar terms together before factoring.
Steps for Factoring an Expression With
More Than One Common Variable or Term
1.) Once you realize that there is no GCF for
an expression, “group” the few terms in
the expression that do have a common
term or variable.
2.) For each group of terms that have a
common factor, factor their GCF using the
distributive property.
3.) Look for a common factor (of more than
one term or variable) for both groupings.
Example: ax – ay – 5x + 5y
Example #3: Factor each expression.
a) 2b(b+4) + 5(b+4)
b) 5my +tm +5ny +tn

When a quadratic relation is in standard form, you only know the direction of
______________ and the __________________.

If you factor the quadratic relation in standard form, you can determine the ______________.
Example #4: Given the quadratic relation y = – x2 – 8x,
a.) Express the relation in factored form.
b.) Determine the zeros.
c.) Determine the vertex.
d.) Sketch the graph.
Example: Two parabolas are defined by y = x2 - 12x and y = - 5x2 + 50x. What is the distance
between their maximum and minimum values (vertexes)?
o
Common factor Equation 1
o
Determine the zeros of Equation 1
o
Determine the max/min (vertex) of Equation 1
o
Common factor Equation 2
o
Determine the zeros of Equation 2
o
Determine the max/min (vertex) of Equation 2
o
Calculate the distance between the maximum and minimum
Remember: Given the two points (x1, y1) and (x2, y2), the distance between these points is
given by the formula:
Homework: p. 203-204 #4ac, 5df, 6be, 7abf, 8bce, 9cef, 10 - 12, 14, 16