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; x = 3
Identify the coefficient in each term.
5. 4x y3
7. 2n –s4 7 13 2 69 1 4 2 -1

2. Lesson 7.6 Polynomials

3. California
Standards
Preparation for Students add, subtract, multiply, and divide monomials and polynomials. Student solve multistep problems, including word problems, by using these techniques.

4. Words to Know Monomial- Polynomial- Binomials - Two terms Trinomials
Single term consisting of numbers,
variables, and whole number exponents.
single
Polynomial-
An expression consisting of two or more
monomial terms that can’t be combined.
many
Types of Polynomials
Binomials
- Two terms
No negative powers
No variables in the denominator
Trinomials
- Three terms

5. Identify each expression as a monomial, binomial,
trinomial, or polynomial. (More than one may apply.)
Binomial
, Polynomial
Polynomial
Trinomial
, Polynomial
Binomial
, Polynomial
Monomial
Trinomial
, Polynomial

6. Standard Form of the Polynomial
- Powers of the variable written in decreasing order.
Non-standard Form
Standard Form

7. You try!
Write the polynomials below in standard form.

8. The degree of a polynomial is the degree of the term with the greatest degree.
When written in standard form, the coefficient of the first term is called the leading coefficient.

9. Write the polynomial in standard form
Write the polynomial in standard form. Then give the leading coefficient.
6x – 7x5 + 4x2 + 9
Find the degree of each term. Then arrange them in descending order:
6x – 7x5 + 4x2 + 9
–7x5 + 4x2 + 6x + 9
Degree 1 5 2
–7x5 + 4x2 + 6x + 9.
The standard form is
The leadingcoefficient is –7.

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

11. Now you try…
Write the polynomial in standard form. Then give the leading coefficient.
18y5 – 3y8 + 14y
Find the degree of each term. Then arrange them in descending order:
18y5 – 3y8 + 14y
–3y8 + 18y5 + 14y
Degree 5 8 1
The standard form is
The leading coefficient is –3.
–3y8 + 18y5 + 14y.

12. Simplifying Polynomials
- Simplified by combining like terms.
Simplify the polynomials below. Write them in
standard form.

13. Simplify the following polynomials. Write in
standard form.

14. Simplify the following polynomials. Write in
standard form.
Answers

15. A root of a polynomial in one variable is a value of the variable for which the polynomial is equal to 0.

16. Identifying Roots of Polynomials
Tell whether each number is a root of 3x2 – 48.
A. 4
B. 0
3x2 – 48
3(4)2 – 48
3x2 – 48
3(0)2 – 48
Substitute for x.
3(16) – 48
48 – 48
3(0) – 48
0 – 48
Simplify. 
–48 
4 is a root of 3x2 – 48.
0 is not a root of 3x2 – 48.

17. Application
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?
Substitute the time for t to find the lip balm’s height.
–16t
The time is 3 seconds.
–16(3)
–16(9) + 200
Evaluate the polynomial by using the order of operations. –
76 feet

18. Find the degree of each polynomial. 1. 7a3b2 – 2a4 + 4b – 15
Lesson Quiz: Part I
Find the degree of each polynomial.
1. 7a3b2 – 2a4 + 4b – 15
2. 25x2 – 3x4
Write each polynomial in standard form. Then give the leading coefficient.
3. 24g g5 – g2
4. 14 – x4 + 3x2 5 4
7g5 + 24g3 – g2 + 10; 7
–x4 + 3x2 + 14; –1

19. Lesson Quiz: Part II
Tell whether each number is a root of 3p2 –
5. 2
yes
6. –2 no

20. Lesson Quiz: Part III
7. The polynomial 3.675v v2 is used to estimate the stopping distance in feet for a car whose speed is v miles per hour on flat, dry pavement. What is the stopping distance for a car traveling at 70 miles per hour? ft