Warm Up
Evaluate each expression for the given value of x.
1.
2x + 3; x = 2
2.
x2 + 4; x = –3
3. –4x – 2; x = –1
y3
7.
4. 7x2 + 2x; x = 3
Identify the coefficient in each term.
5.
4x3
6.
2n7
8.
–s4
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Algebra/Lesson 6-3: Polynomials
Objectives:


Classify polynomials and write polynomials in standard form.
Evaluate polynomial expressions.
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.
Example 1: Find the degree of each monomial.
A.
4p4q3
C.
3
B.
7ed
1
C.I.O.-Example 1: Find the degree of each monomial.
a.
1.5k2m
b.
4x
c.
2c3
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.
Example 2: Find the degree of each polynomial.
A.
11x7 + 3x3
B.
C.I.O.-Example 2: Find the degree of each polynomial.
a.
5x – 6
b.
x3y2 + x2y3 – x4 + 2
The terms of a polynomial may be written in any order. However, 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.
Example 3:
A. Write the polynomial in standard form. Then give the leading coefficient.
6x – 7x5 + 4x2 + 9
2
B. Write the polynomial in standard form. Then give the leading coefficient.
y2 + y6 – 3y
C.I.O.-Example 3: Write the polynomial in standard form. Then give the leading coefficient.
a.
16 – 4x2 + x5 + 9x3
b.
18y5 – 3y8 + 14y
Some polynomials have special names based on their degree and the number of terms they have.
3
Example 4: Classify each polynomial according to its degree and number of terms.
A.
5n3 + 4n
C.
–2x
B.
4y6 – 5y3 + 2y – 9
C.I.O.-Example 4: Classify each polynomial according to its degree and number of terms.
a.
x3 + x2 – x + 2
b.
6
c.
–3y8 + 18y5 + 14y
Example 5:
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 –16t2 + 220, where t is time in seconds. How far above the water will the lip balm be after 3
seconds?
After 3 seconds the lip balm will be 76 feet from
the water.
C.I.O.-Example 4:
What if…? Another firework with a 5-second fuse is launched from the same platform at a speed of 400 feet per second. Its height is
given by –16t2 +400t + 6. How high will this firework be when it explodes?
4
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.
24g3 + 10 + 7g5 – g2
4.
14 – x4 + 3x2
Lesson Quiz: Part II
Classify each polynomial according to its degree and number of terms.
5.
18x2 – 12x + 5
6.
2x4 – 1
7. The polynomial 3.675v + 0.096v2 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?
p. 409: 27-57 odd, 58-62
58) 196.65 ft
60) sometimes
62) sometimes
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