Lesson 7-4 Polynomials
Example 1 Identify Polynomials
Determine whether each expression is a polynomial. If so, identify the polynomial as a monomial,
binomial, or trinomial.
Expression
Is it a Polynomial?
Monomial, Binomial,
or Trinomial?
a.
3x
4
3x 3
Yes; 4 = 4x.
monomial
b.
1 2
2a + 2b – 1
1
1
Yes; 2a2 + 2b – 1 = 2a2 + 2b + (-1), the
trinomial
2j2
k +2
r2s3 – 2r3st
sum of three monomials.
2j2
No; k is not a monomial.
Yes; r2s3 – 2r3st = r2s3 + (-2r3st), the
sum of two monomials.
c.
d.
Example 2 Degree of a Polynomial
Find the degree of each polynomial.
a. 2xy – x2yz2
Step 1 Find the degree of each term.
2xy: degree = 1 + 1 or 2
Step 2
none of these
binomial
x2yz2: degree = 2 + 1 + 2 or 5
The degree of the polynomial is the greater degree, 5.
b. x + 3x2 – 2
x: degree = 1
2: degree = 0
3x2: degree = 2
The degree of the polynomial is 2.
c. 5r2s – 6r + 2rs – 1
5r2s: degree = 2 + 1 or 3
2rs: degree = 1 + 1 or 2
6r: degree = 1
1: degree = 0
The degree of the polynomial is 3.
Example 3 Standard Form of a Polynomial
Write each polynomial in standard form. Identify the leading coefficient.
a. –2x2 + 1 + 3x3
Step 1 Find the degree of each term.
Polynomial: –2x2 + 1 + 3x3
Degree:
2
0
3
Step 2 Write the terms in descending order: 3x3 – 2x2 + 1.
The leading coefficient is 3.
b. 21 – a3 + 4a2 – 7a
Step 1 Polynomial: 21 – a3 + 4a2 – 7a
Degree:
0 3
2
1
Step 2 Write the terms in descending order: –a3 + 4a2 – 7a + 21
The leading coefficient is –1.
Real-World Example 4 Use a Polynomial
SWINGS The height in feet of a swing can be modeled by the equation
H = 0.3t2 + 0.1t + 2, where t is the time in seconds. How high is the swing
after 3 seconds?
Substitute the value of t to find the height of the swing after 3 seconds.
H = 0.3t2 + 0.1t + 2
= 0.3(3)2 + 0.1(3) + 2
= 2.7 + 0.3 + 2
=5
Original equation.
t=3
Simplify.
Add.
The height of the swing after 3 seconds is 5 feet.