WHRHS
2012-2013
Unit 3 – Polynomials
Algebra 2CP
Unit 3 Day A ~ Polynomials
 Monomial - a Number, a Variable or a PRODUCT of a number and a variable.
*monomials cannot have radicals with variables inside, quotients of
variables or variables with negative exponents.
 Degree of a monomial - is the SUM of the exponents of the variable(s) in the monomial. The degree of
a constant term is 0.
 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.)
 Constant Term of Polynomial – Term that does not have a variable attached to it.
 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
WHRHS
2012-2013
Unit 3 – Polynomials
Algebra 2CP
Part 1: Find the degree of the polynomial.
1. 3x  2
2. 4 x 3  17 x  5
3. 13x n  5 x n  2
4. 0.55 x 2  0.7 x
5. 7 x3  10 x  15
Part 2: Standard form of a polynomial is when the terms are written so that the exponents on the
variables decrease from left to right.
Write the polynomial in standard form.
6. 3x 2  x  3x3  12 
7. 4  x3  3 x 2 
8. 4 x  5  2 x 2 
9. 7  6 x  3x 2  x 3 
Like terms in a polynomial have the same _____________ and the same ___________.
Part 3: Identify the like terms and simplify the expression.
10.
x 2  5 x3  2 x  3x 2  7  4 x  7
11. 6  x  2 x
12. 2 x
2
13. 15 x
2
 5  x2
 5 x3  x 2  18  5 x  3x3
8
 4 x3  6 x  15  x 7  2 x
Part 4: Leading Coefficient and Constant Term.
Identify the leading coefficient in each of the polynomials in part 3.
10. _____
11. _____
12. _____
13. _____
Identify the constant term in each of the polynomials in part 3.
10. _____
11. _____
12. _____
13. _____
WHRHS
2012-2013
Unit 3 – Polynomials
Algebra 2CP
Adding and Subtracting Polynomials
To add polynomials – simply combine like terms!!
Horizontal Format:
1. (3x2 + 2x - 7) + (7x3 – 3 + 4x2) =
2. (4x2 + 5x – 3) + (7x3 – 7x + 1) =
Vertical Format:
3. (2x – 3x2 + 4x3 + 1) + (3x2 – 2x + 7)
4. (5x4 – 2x + x2 + 4) + (-5 + 6x)
To subtract polynomials – distribute the negative and then add!!
(*Think – subtraction means add the opposite*)
Horizontal Format:
5. (3x2 – 7xy + y2) – (-4x2 + 7xy – 3y2)
6. (6x3 – 3x + 7) – (3x2 – 5x + 12)
Vertical Format:
6. (3x2 – 2x + 5) – (2 – 3x + 4x3)
7. (5x2 + 3x – 1) – (2x2 + 4x – 6)
WHRHS
2012-2013
Unit 3 – Polynomials
Algebra 2CP
Unit 3 ~ Day A HW
Complete the chart below by first rewriting each polynomial in standard form. Then identify the
degree, leading coefficient, and constant for each polynomial.
Leading
Polynomial
Rewrite in Standard Form
Degree
Constant
Coefficient
1. -2 + 5x
2. 12
3. -1 – 4x2 + 7x
4. 5x3 – 2
5. 4 – 3x4
6. x2 + 5x + 2x4 – x+1
7.
3x3 – 10x + 15 +
6x5
8. 7x – x5 + 3x2 +3x5
9. 6 – 3x3
10.
5x + 14x4 – 8 – 4x
+ 2x2
WHRHS
2012-2013
Check the box(es) that describes each polynomial below.
Monomial
Binomial
Unit 3 – Polynomials
Algebra 2CP
Trinomial
11. x2 – 5x + 7
12. 10x4
13. 3 – 15x3
14. 10x5 – 12x3 + 8
15. 6x9 – 10x5 + 2x – 19
Add or subtract each polynomial. Choose a method (horizontal/vertical):
16. (4x2 + 3x – 5) + (x2 – 7x + 10)
17. (x2 – 2x + 7) – (3x2 – 4x + 7)
18. (4a2 – 7a) – (-6a2 + 5a – 7)
19. (5x2 – 3x + 8) – (x2 – 8x + 12)
20. (3x2 - 2x + 7) + (-3x2 + 2x – 12)
21. (5x2 – x + 6) + (-3x2 + 2x – 12) + (-6x2 + 5x – 7)
Polynomial