Math 10C
Polynomials: Lesson #5
Factoring Polynomials : GCF
Objective: By the end of this lesson, you will be able to:
- Find factors of a polynomial using tiles or drawings
- Find the GCF of a polynomial
- Factor a polynomial using the GCF
Factoring polynomials is the opposite of __________________ polynomials:

With multiplying, we started with the ________________ (_______________________)
and found the _________________ (___________).

With factoring, we will start with the _________________ (_________) and find the
_______________ (_________________________).
We have seen that one method to factor is by building a rectangle out of algebra tiles.
e.g. 1) Consider the algebra tile diagram shown below:
a) Write the polynomial represented by the area.
b) Write the dimensions (factors) of the polynomial.
We can do this symbolically by finding the ________________________________________ of
all the terms in a polynomial:
e.g. 2) What is the greatest common factor of:
a) 18 y and 30 y 2 ?
b) 4a 2 b 3 , 17a 4b2 , and 6a 3 ?
Math 10C
Polynomials: Lesson #5
Once you have found the greatest common factor of each term in the polynomial, ____________
each of the terms by the GCF to find the other factor.
e.g. 3) Factor the following polynomials:
a) 40n2  32n
b)  9 x2  15x  3
* If the first term is negative, the GCF
will also be negative.
c) 8x5 y  x3 y 2  24 x 2 y 6
How could you check your answer?
e.g. 4) Check your answer for e.g. 3b).
e.g. 5) The surface area of a cylinder is given by the formula A  2r 2  2rh , where r is the
radius of the base and h is the height of the cylinder. Write the formula for A in factored
form.
r
h
Assignment:
p. 155-156 #7, 10, 12, 14, 16, 18