Download the review sheet for test #5

Algebra Concepts Test #5 Review
Page 1 of 4
Section 5.1: The Product and Power Rules for Exponents
Rule Name
Product Rule
Rule
a m  a n  a mn
a 
 a mn
3 
 ab 
 a mb m
2 p
m n
Power Rules
Example
6 2  6 4  6 2  4  66
m
2 4
m
5
 32(4)  38
 25 p 5
2
am
a
   m
b
b
2
5 5
   2
 3 3
Section 5.2: Integer Exponents and the Quotient Rule
Big Idea: There are shortcut formulas to doing calculations with exponents. These rules help us simplify
expressions to make equation solving easier.
Rules for Exponents:
For positive integers m and n and any nonzero real numbers a and b:
Rule Name
Zero Exponent Definition
Negative Exponent Definition
Rule
a0  1
am
bn
m
a
b
   
b
a
m
a
 a mn
n
a
Quotient Rule
1
1
an
bn
 m
a
an 
Negative to Positive Rules
4
Example
170 = 1; (-4)0 = 1
1 1
32  2 
3
9
5
2
3
4
 5
2
4
3
a 1b 2 
 3a
 5a
b 
2
3 5 2

5
m
3 4 2
b

4
1
1
  5a
1 2 2
a b
  3a
3 4 2
b
2
2 4
2

3 5 2
1
4 a b 5 a 6b8 32 a 6b 10
42 a 2b 4 a 6 a 6b10

52 b8 32
42 a14b14
 2 2 8
3 5 b
42 a14b 6
 2 2
3 5

5
 2
 3
   
 3
 2
8
2
 283  25
3
2
b
Algebra Concepts Test #5 Review
Page 2 of 4
Section 5.3: An Application of Exponents: Scientific Notation
Examples:
4,280 = 4.28  103
93,000,000 = 9.3  107
753,658,554  7.54  109
128,000,000,000,000 = 1.28  1014
2.2  102 = 220
4.56  108 = 456,000,000
0.032 = 3.2  10-2
0.000 259 828  2.60  10-4
0.000 000 089 = 8.9  10-8
0.000 000 000 000 001 = 1  10-15
7.2  10-3 = 0.007 2
8.975  10-6 = 0.000 008 975
1. Converting from numbers to scientific notation:
Move the decimal until it is just behind the first nonzero digit.
The number of times you moved the decimal is the exponent on 10. The sign of the exponent will be positive
fro big numbers, negative for small decimals.
2. Converting from scientific notation to numbers:
For positive exponents, move the decimal to the right a number of times equal to the exponent on 10.
For negative exponents, move the decimal to the left a number of times equal to the exponent on 10.
3. Scientific Notation on your calculator:
Use the EE or EXP button: 3.810-6 = 3.8 EE -6
4. Calculating with scientific notation:
Use your calculator to punch it in, or use the rules of exponents to work it out:
 9.5 10   3.6 10   9.5
2 2
5 103
1
104  3.6 10 1
5 103
9.52  3.6 104 10 1


5
103
 64.98 104 ( 1)( 3)
2
 64.98 102
 6.498 10 102
 6.48 101
Algebra Concepts Test #5 Review
Page 3 of 4
Section 5.4: Adding and Subtracting Polynomials; Graphing Simple Polynomials
Polynomial vocabulary:
A polynomial in x is a sum of finite terms of the form axn.
Example: 4x3 + 6x2 – 5x – 8
Notice that the polynomial is written in descending powers of the variable.
The coefficient of any term is the number part
The degree of a term is the exponent on the variable.
The degree of a polynomial is the greatest exponent.
A polynomial with one term is called a monomial.
A polynomial with two terms is called a binomial.
A polynomial with three terms is called a trinomial.
Polynomials with more terms aren’t usually given specific names.
When adding or subtracting polynomials, you can only combine like terms.
Example of evaluating polynomials: if the function P(x) = 5x2 + 3x – 7, then P(2) = 5(2)2 + 3(2) – 7 = 5(4) + 6 –
7 = 19
The graph of a polynomial of degree 2 (i.e., a quadratic polynomial) always looks like a parabola.
1
Here is a graph of equation y   x 2  x :
64
Algebra Concepts Test #5 Review
Page 4 of 4
Section 5.5: Multiplying Polynomials
Multiplying two monomials: Use the rules of exponents to combine common bases.
(-8p3q6)(-9p2q2) = (-8)(-9)(p3p2)(q6q2) = 728p5q8
Multiplying a monomial and a polynomial: Use the distributive property.
-5x3(2x3 + 4x2 – 7x – 9) = -10x6 – 8x5 + 35x4 + 45
Multiplying two binomials: Use the FOIL acronym: multiply FIRST terms, then OUTSIDE terms, then
INSIDE terms, then LAST terms. This method ONLY WORKS FOR BINOMIALS!
Multiplying two polynomials: Multiply every term of the first polynomial with every term of the second
polynomial, and then add up the products. There are three techniques for doing this:
1. Technique #1 for multiplying two polynomials: Write out every combination of products, then
combine like terms.
2. Technique #2 for multiplying two polynomials: Write out the multiplication vertically, then carry it
out like a long-hand numerical multiplication problem.
3. Technique #3 for multiplying two polynomials: Write out the polynomials on a grid, multiply out
each pair of monomials, then add like terms.
Section 5.6: Special Products (of Polynomials)
2
 x  y   x 2  2 xy  y 2
 x  y   x 2  2 xy  y 2
 x  y  x  y   x2  y 2
2