1. Warm Up Evaluate each expression for the given value of x.
1. 2x + 3; x = x2 + 4; x = –3
3. –4x – 2; x = –1 4. 7x2 + 2x = 3
Identify the coefficient in each term.
5. 4x y3
7. 2n –54 7 13 2 69 4 1 2 –1

2. Graph the line given the slope and y-intercept.

3. Objectives
Classify polynomials and write polynomials in standard form.
Evaluate polynomial expressions.

4. A monomial is a number, a variable, or a product of numbers and variables with whole-number exponents.
The degree of a monomial is the sum of the exponents of the variables. A constant has degree 0.

5. Find the degree of each monomial.
1.5k2m A.
4p4q3 3 7
B. 7ed E. 4x 1 2
C. 3 F.
2c3 3
The degree of a monomial is the sum of the exponents of the variables. A constant has degree 0.

6. The terms of an expression are the parts being added or subtracted
The terms of an expression are the parts being added or subtracted. See Lesson 1-7.
Remember!

7. A polynomial is a monomial or a sum or difference of monomials.
The degree of a polynomial is the degree of the term with the greatest degree.

8. Find the degree of each polynomial.
A. 11x7 + 3x3
D. x3y2 + x2y3 – x4 + 2 7 5 B. 4
C. 5x – 6 1
The degree of a polynomial is the degree of the term with the greatest degree.

9. Polynomials that contain only one variable are usually written in standard form.
The standard form of a polynomial that contains one variable is written with the terms in order from greatest degree to least degree. When written in standard form, the coefficient of the first term is called the leading coefficient.

10. Write the polynomial in standard form
Write the polynomial in standard form. Then give the leading coefficient.
6x – 7x5 + 4x2 + 9
–7x5 + 4x2 + 6x + 9
Degree 1 5 2

11. A variable written without a coefficient has a coefficient of 1.
Remember!
y5 = 1y5

12. Write the polynomial in standard form
Write the polynomial in standard form. Then give the leading coefficient.
y2 + y6 – 3y
y6 + y2 – 3y
Degree 2 6 1

13. Write the polynomial in standard form
Write the polynomial in standard form. Then give the leading coefficient.
16 – 4x2 + x5 + 9x3
x5 + 9x3 – 4x2 + 16
Degree 2 5 3

14. Write the polynomial in standard form
Write the polynomial in standard form. Then give the leading coefficient.
18y5 – 3y8 + 14y
–3y8 + 18y5 + 14y
Degree 5 8 1

15. Some polynomials have special names based on their degree and the number of terms they have.
Monomial
Binomial
Trinomial
Polynomial
4 or more 1 2 3 1 2
Constant
Linear
Quadratic 3 4 5
6 or more
6th,7th,degree and so on
Cubic
Quartic
Quintic
Problem 1
Problem 2

16. Classify each polynomial according to its degree and number of terms.
A. 5n3 + 4n
Degree 3 Terms 2
cubic binomial
B. 4y6 – 5y3 + 2y – 9
4y6 – 5y3 + 2y – 9 is a
6th-degree polynomial
Degree 6 Terms 4
C. –2x
Degree 1 Terms 1
linear monomial.
Tables

17. Classify each polynomial according to its degree and number of terms.
a. x3 + x2 – x + 2
Degree 3 Terms 4
cubic polymial
b. 6
constant monomial
Degree 0 Terms 1
c. –3y8 + 18y5 + 14y
Degree 8 Terms 3
8th-degree trinomial
Tables

18. A tourist accidentally drops her lip balm off the Golden Gate Bridge
A tourist accidentally drops her lip balm off the Golden Gate Bridge. The bridge is 220 feet from the water of the bay. The height of the lip balm is given by the polynomial –16t , where t is time in seconds. How far above the water will the lip balm be after 3 seconds?
–16t
–16(3)
–16(9) + 220 – 76
feet