Download 14-1 - Maple Heights City Schools

14-1
14-1Polynomials
Polynomials
Warm Up
Problem of the Day
Lesson Presentation
Course3 3
Course
14-1 Polynomials
Warm Up
Identify the base and exponent of each
power.
1. 34 3; 4
2. 2a 2; a
3. x5
x; 5
Determine whether each number is a
whole number.
yes
4. 0 yes
5. –3 no
6. 5
Course 3
14-1 Polynomials
Problem of the Day
If you take a whole number n, raise it to
the third power, and then divide the
result by n, what is the resulting
expression?
n2
Course 3
14-1 Polynomials
Learn to classify polynomials by degree
and by the number of terms.
Course 3
14-1 Polynomials
Vocabulary
monomial
polynomial
binomial
trinomial
degree of a polynomial
Course 3
14-1 Polynomials
The simplest type of polynomial is called a
monomial. A monomial is a number or a
product of numbers and variables with
exponents that are whole numbers.
Course 3
14-1 Polynomials
Additional Example 1: Identifying Monomials
Determine whether each expression is a
monomial.
A. √2
•
x3y4
monomial
3 and 4 are whole
numbers.
Course 3
B. 3x3√y
not a monomial
y does not have a
exponent that is a whole
number.
14-1 Polynomials
Check It Out: Example 1
Determine whether each expression is a
monomial.
A. 2w
Course 3
•
p3y8
B. 9t3.2z
monomial
not a monomial
3 and 8 are whole
numbers.
3.2 is not a
whole number.
14-1 Polynomials
A polynomial is one monomial or the sum
or difference of monomials. Polynomials
can be classified by the number of terms.
A monomial has 1 term, a binomial has 2
terms, and a trinomial has 3 terms.
Course 3
14-1 Polynomials
Additional Example 2: Classifying Polynomials
by the Number of Terms
Classify each expression as a monomial, a
binomial, a trinomial, or not a polynomial.
A. xy2
monomial
Polynomial with 1 term.
B. 2x2 – 4y–2
not a polynomial
–2 is not a whole number.
C. 3x5 + 2.2x2 – 4
trinomial
Polynomial with 3 terms.
D. a2 + b2
binomial
Polynomial with 2 terms.
Course 3
14-1 Polynomials
Check it Out: Example 2
Classify each expression as a monomial, a
binomial, a trinomial, or not a polynomial.
A. 4x2 + 7z4
binomial
Polynomial with 2 terms.
B. 1.3x2.5 – 4y
not a polynomial
2.5 is not a whole number.
C. 6.3x2
monomial
Polynomial with 1 term.
D. c99 + p3
binomial
Polynomial with 2 terms.
Course 3
14-1 Polynomials
The degree of a term is the sum of the
exponents of the variables in the term. The
degree of a polynomial is the same as the
term with the greatest degree.
4x2
Degree 2
+
2x5
+
Degree 5
xy
Degree 1
Degree 5
Course 3
+
5
Degree 0
14-1 Polynomials
Additional Example 3: Classifying Polynomials
by Their Degrees
Find the degree of each polynomial.
A. x + 4
x
+
4
Degree 1 Degree 0
The degree of x + 4 is 1.
B. 5x – 2x2 + 6
5x
–
2x2
+
6
Degree 1
Degree 2
Degree 0
The degree of 5x – 2x2 + 6 is 2.
Course 3
14-1 Polynomials
Check It Out: Example 3
Find the degree of each polynomial.
A. y + 9.9
y
+
9.9
Degree 1 Degree 0
The degree of y + 9.9 is 1.
B. x + 4x4 + 2y
x
+
4x4
+
2y
Degree 1
Degree 4
Degree 1
The degree of x + 4x4 + 2y is 4.
Course 3
14-1 Polynomials
Additional Example 4: Physics Application
The height in feet after t seconds of a rocket
launched straight up into the air from a 40-foot
platform at velocity v is given by the polynomial
–16t2 + vt + 40. Find the height after 10 seconds
of a rocket launched at a velocity of 275 ft/s.
Write the polynomial
–16t
+ vt
+ s
expression for height.
–16(10)2 + 275(10) + 40 Substitute 10 for t, 275
for v, and 40 for s.
–1600 + 2750 + 40
Simplify.
1190
The rocket is 1190 ft high 10 seconds after launching.
Course 3
14-1 Polynomials
Check It Out: Example 4
The height in feet after t seconds of a rocket
launched straight up into the air from a 20-foot
platform at velocity v is given by the polynomial
-16t2 + vt + s. Find the height after 15 seconds
of a rocket launched at a velocity of 250 ft/s.
Write the polynomial
2
–16t
+ vt
+s
expression for height.
–16(15)2 + 250(15) + 20 Substitute 15 for t, 250
for v, and 20 for s.
–3600 + 3750 + 20
Simplify.
170
The rocket is 170 ft high 15 seconds after launching.
Course 3
14-1 Polynomials
Lesson Quiz
Determine whether each expression is a
monomial.
1. 5a2z4 yes
2. 3√x
no
Classify each expression as a monomial, a
binomial, a trinomial, or not a polynomial.
3. 2x2 – 3x – 6
4. 3m3+ 4m
trinomial
binomial
Find the degree of each polynomial.
5. 3a2 + a5 + 26 5
Course 3
6. 2c3 – c2 3