Name:________________________
Algebra 1
Identifying Polynomials – Adding, Subtracting, Multiplying Polynomials – Perimeter and Area
A monomial is a number, a variable, or the product of a number and one or more variables with whole number
exponents. The degree of a monomial is the sum of the exponents of the variables in the monomial.
A polynomial is a monomial or a sum of monomials, each called a term of the polynomial. The degree of a
polynomial is the greatest degree of its terms. Polynomials cannot have negative exponents, variable
exponents, or variables in the denominator.
Like terms are terms that have the same variables with the same exponents.
Polynomials are written so that the exponents of a variable decrease from left to right.
Leading coefficient
Degree
Constant term
2x3 + x2 – 5x + 12
Function Type
Linear
Quadratic
Cubic
Quartic
Polynomial Name
Polynomial
Monomial
Binomial
Trinomial
Degree
1
2
3
4
Example
3x + 1
5x2 – 6x – 7
8x3 + 2x2 – 5x + 3
4
6x + 5x3 – 8x2 – 2x + 4
Number of terms, t
t>1
t=1
t=2
t=3
Example
2x5 + 4x3 – 2x + 1
6x3y2z7
8x - 3
3
5x – 4x2 + 7
1. Tell whether or not each expression below is a polynomial. If yes, name the polynomial. If no, then explain
why it is not a polynomial.
1.a.) 8
1.b.) 4x2 – 5x + 1
1.c.) 6x2 – 5xy
1.d.) 4x-2 + 5
2. Identify each expression below as a monomial, binomial, trinomial, or polynomial. Identify each expression
as linear, quadratic, cubic, or quartic.
2.a.) 7x2 – 5
2.b.) 9x
2.c.) 6x3 – 5x2 – 1
2.d.) 7x4 – 2x2 + 4x – 5
3. If not written correctly, write in correct degree order. Then list the degree, type of polynomial, and the
leading coefficient.
6𝑥 2 − 7𝑥 + 3
9𝑥 − 8𝑥 4 + 5𝑥 2
Degree:_____
Degree:_____
Type: _________________
Type: _____________________
Leading coefficient: ______
Leading coefficient: _____
9𝑥 7
7𝑥 2 − 9𝑥 5 + 8𝑥 4 − 11𝑥 + 9
Degree:_____
Degree:_____
Type: _________________
Type: _____________________
Leading coefficient: ______
Leading coefficient: ______
12x
6𝑥 2 𝑦 3 + 7𝑥 4
Degree:_____
Degree:_____
Type: _________________
Type: _____________________
Leading coefficient: ______
Leading coefficient: ______
4. Add or subtract the following polynomials:
(3x 2  5x  9)  (8x  9 x 2  11)
(5x 3  6x 4  9 x  1)  (3x 3  5x 4  3)
(3x2 – 5x + 8) + (2x2 – 6x – 7)
(7𝑥 − 11𝑥 2 − 9) + (8𝑥 2 − 6𝑥 − 5)
(9𝑥 − 5𝑥 2 − 8) − (−3𝑥 + 7𝑥 2 − 12)
(-4x2 + 8x – 7) – (3x2 – 11x – 5)
5. Write a polynomial that represents the perimeter of the figure.
Perimeter:__________________
Perimeter: ___________________
3x2 + 5x – 2
9x + 5
5x + 1
8x2 – 3
Perimeter:__________________
Perimeter: ___________________
6. Multiply. State the degree, leading coefficient, and type of polynomial.

 7 x3 8 x  4 x 2  8 x3  2

(8𝑥 − 5)(2𝑥 − 9)
Degree:_____
Degree:_____
Leading coefficient: ______
Leading coefficient: ______
Polynomial Type: _________________
Polynomial Type: _________________
(2𝑥 + 4)(6𝑥 2 − 7𝑥 − 3)
(3𝑥 + 5)2
Degree:_____
Degree:_____
Leading coefficient: ______
Leading coefficient: ______
Polynomial Type: _________________
Polynomial Type: _________________
7. Find the perimeter and area for each.
3x  5
8x  2
5x  3
3x  1
6x  1
11x  4
Perimeter: __________________
Perimeter: ________________
Area: ______________________
Area: ____________________