Factoring Polynomials
Step 1: Factor out the Greatest Common Factor (GCF)
32 x 3 24 x 2 + 16
gcf = 8;
factored: 8(4 x 2 3 x + 2)
18 x 3 24 x 2
Examples:
gcf = 6 x 2
factored: 6 x 2 (3x + 4)
1. 28 x 6 + 35 x 4
8. 30 x 6 45 x 5 + 60 x 3
2. 28 x 6 36 x 3
9.
MAT 105
Multiplying Polynomials
Do each of the multiplications below, collect like terms, and put your answers in standard form.
Note: 1-4 intentionally contain slightly different problems. As you do them, and analyze them to
see how the products are diff
MAT 105
Spring 2011
Final Exam
Name_
Part I
No Calculators
Show Work to Receive Credit
Score _ / 250
Extra Credit: (5 pts) State the Quadratic Formula
for solving quadratic equations in the form
ax2 + bx + c = 0
1. (25 pts) Perform the indicated operation
MAT 105 Adding and Subtracting Fractions
When adding and subtracting fractions, you must have a common denominator: same size pieces.
Then you just add the numerators: the number of pieces.
When you are getting a common denominator, it is like cutting the
Beginning Exponents (answers on next page)
1. The meaning of x7 is _.
2. In 2 6
a. 2 is called the _, and
b. 6 is called the _.
3. When multiplying with the same base, as in x 7 x 8 , the shortcut is:
_, so x 7 x 8 = _.
m 2 m3 =
_. v 3 v 4 = _.
4. When di
MAT 105
Adding and Subtracting Polynomials
Perform the following operations. Collect like terms, and put your final answer in standard form.
1.
(7 x
3
+ 2 x 2 4 x + 8 + 2 x 3 6 x 2 + 5x + 3
)(
2.
(6 x
3
+ 3x 2 3x + 4 + 10 x 3 5 x 6
3.
(x
4.
( 5x
4
5.
(4 x
MAT 105 Notebook and Math Study Skills
Name _
Notebook Checks : 5% of your semester grade. (1st check at Test 1, 2nd check at Test 2)
I will be looking for the following:
Point values:
1. Your name on the front
1
2. Your contact information (e-mail and ce
Factoring Numbers:
Vocabulary:
The number 36 is a multiple of 4;
The number 36 is divisible by 4.
The number 4 is a factor of 36.
The product of 3 and 6 is 18.
A prime number has exactly 2 positive integer factors: 1 and itself.
The prime numbers are 2, 3
Listing all the (Positive Integer) Factors of a Number
First, list the pairs of factors whose product is the number. Dont do this in a haphazard order,
but begin with 1 times the number, then try 2, 3, etc. Stop when the next number you would try
has alre