Unit 2 – Exponential Expressions & Polynomials
Algebra 2A
WHRHS
2011-2012
Unit 2 Day B ~ Scientific Notation & Polynomials
 Scientific Notation – A number expressed in the form:
m 10n where 1  m  10 and n is an Integer !
 Polynomials – a variable expression whose terms are Monomials. Monomials
have 1 term. Binomials have 2 terms. Trinomials have 3 terms. Polynomials
with more than 3 terms do not have special names. Polynomials in one variable
are usually arranged in descending order so that the exponents of the variables
decrease from left to right.
*polynomials(just like monomials) cannot have radicals with variables inside,
quotients of variables or variables with negative exponents.
 Degree of Polynomial – is the Greatest of the degrees of any of its terms.
(Remember each term is a monomial so the degree will be the sum of the
exponents in the monomial.)
 Leading Coefficient of Polynomial – is the coefficient of the variable with the
largest exponent.
What Can You Do With Polynomials?
 Evaluate Polynomials – Just substitute in the assigned value for the variable and
find the value of the polynomial.
Example: 3x 2  4 x  6 evaluate x = 3. The value of the polynomial will be 45.
3(3)2 + 4(3) + 6 = 45.
 Add Polynomials – To add polynomials just Combine like terms. There are 2
formats you can use to add polynomials – horizontal format or vertical format.
Example: Horizontal Format:( 3x 2  4 x  6 ) + ( 7 x 2  2 x  2 ) = 10x2 + 6x + 4
Vertical Format
3x 2  4 x  6
+ 7 x2  2 x  2
10x2 + 6x + 4
 Subtract Polynomials – To subtract polynomials just Add the additive inverse of
the 2nd polynomial. There are 2 formats you can use to subtract polynomials –
horizontal format or vertical format.
Example: Horizontal Format :( 3x 2  4 x  6 ) - ( 7 x 2  2 x  2 ) = - 4x2 + 2x + 8
Vertical Format
3x 2  4 x  6
7 x 2  2 x  2
- 4x2 + 2x + 8
Unit 2 – Exponential Expressions & Polynomials
Algebra 2A
WHRHS
2011-2012
 Multiplying a Polynomial by a Monomial –
Use the Distributive Property and the Rules for Multiplying Exponential Expressions.
Example:
- 5x2 (x2 – 2x + 3) = (- 5x2)(x2) + (- 5x2)(- 2x) + (- 5x2)(3) = - 5x4 + 10x3 – 15x2

Multiplying 2 Polynomials – Multiply each term of one polynomial by
each term of the other polynomial and then Combine like terms.
Example: (2x + 1) (x2 – 2x + 3) = 2x3 - 4x2 + 6x + x2 – 2x +3 = 2x3 - 3x2 + 4x + 3
*Efficient method to use when multiplying 2 binomials is called FOIL – it is based on
the Distributive Property and means – multiply 1st terms of each binomial, then
multiply the outer terms of each binomial, then multiply the inner terms of each
binomial, then multiply the last terms of each binomial and then take these
products and combine like terms to solve.
**Polynomials with Special Products –
Sum & Difference of 2 binomials : (a + b)(a – b) = a2 – b2
Square of Binomial: (a + b)2 = (a + b)(a + b) = a2 + 2ab + b2
Scientific Notation Examples:
1.
2.
3.
4.
5.
6.
4006 
320.0 
0.4050 
0.00203 
75, 000 
0.0000702 
7. 4.3 x 10 3 
8. 6.75 x 10 4 
2.64 x 1035
9.

1.32 x 1012
10.
.42 x 10 4

.07 x 10 2
11.
5.5 x 106

.5 x 10 2
Unit 2 – Exponential Expressions & Polynomials
Algebra 2A
WHRHS
2011-2012
Polynomial Examples:
1.
x
2.
 3x
3
 

 3 x 2  x 2  3x  2) 
2
 

 2x 1  4x2  2x  5 

 

3. 3 x 2  2 x  1  5 x 2  x  1 


4. 4mn 8m3  2m 2 n  m 2 n  mn 2  3n3 
5.
 3xy  2 z 
6.
 a  5
7.
 x  2
3
2
2


 7  x  1 
2