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Identify the base and exponent of each power.
1. 34 2. 2a 3. x5
Determine whether each number is a whole number.4. 0 5. –3 6. 5
3; 4 2; a x; 5
yes no yes
Warm Up
Polynomials13.1
Learn to classify polynomials by degree and by the number of terms.
monomialpolynomialbinomialtrinomialdegree of a polynomial
Vocabulary
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.
Monomials2n, x3, 4a4b3, 7
Not monomials
p2.4, 2x, √x, g25
monomial not a monomial
3 and 4 are whole numbers.
Determine whether each expression is a monomial.
y does not have a exponent that is a whole number.
B. 3x3√yA. √2 • x3y4
Example: Identifying Monomials
Determine whether each expression is a monomial.
A. 2w • p3y8 B. 9t3.2z
monomial not a monomial
3 and 8 are whole numbers.
3.2 is not a whole number.
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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 term, and a trinomial has 3 terms.
Classify each expression as a monomial, a binomial, a trinomial, or not a polynomial.
A. xy2
B. 2x2 – 4y–2
C. 3x5 + 2.2x2 – 4
D. a2 + b2
monomial
Polynomial with 1 term.
not a polynomial–2 is not a whole number.
trinomialPolynomial with 3 terms.
binomialPolynomial with 2 terms.
Example: Classifying Polynomials by the Number of Terms
Classify each expression as a monomial, a binomial, a trinomial, or not a polynomial.
A. 4x2 + 7z4
B. 1.3x2.5 – 4y
C. 6.3x2
D. c99 + p3
binomialPolynomial with 2 terms.
not a polynomial2.5 is not a whole number.
monomialPolynomial with 1 term.
binomialPolynomial with 2 terms.
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A polynomial can also be classified by its degree. The degree of a polynomial is the degree of the term with the greatest degree.
4x2 + 2x5 + x + 5
Degree 2 Degree 5 Degree 1 Degree 0
Degree 5
Find the degree of each polynomial.
A. x + 4
B. 5x – 2x2 + 6
Degree 1 Degree 0 x + 4
The degree of x + 4 is 1.
Degree 1 Degree 2 Degree 0 5x – 2x2 + 6
The degree of 5x – 2x2 + 6 is 2.
Examples: Classifying Polynomials by Their Degrees
Find the degree of the polynomial.
C. –3x4 + 8x5 – 4x6
Degree 4 Degree 5 Degree 6
–3x4 + 8x5 – 4x6
The degree of –3x4 + 8x5 – 4x6 is 6.
Example: Classifying Polynomials by Their Degrees
Find the degree of each polynomial.
A. y + 9.9
B. x + 4x4 + 2y
Degree 1 Degree 0 y + 9.9
The degree of y + 9.9 is 1.
Degree 1 Degree 4 Degree 1 x + 4x4 + 2y
The degree of x + 4x4 + 2y is 4.
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Find the degree of each polynomial.
C. –6x4 – 9x8 + x2
Degree 4 Degree 8 Degree 2
–6x4 – 9x8 + x2
The degree of –6x4 – 9x8 + x2 is 8.
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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 + s. Find the height after 10 seconds of a rocket launched at a velocity of 275 ft/s.
Write the polynomial expression for height. –16t + vt + s
–1600 + 2750 + 40
–16(10)2 + 275(10) + 40 Substitute 10 for t, 275 for v, and 40 for s. Simplify.
1190
The rocket is 1190 ft high 10 seconds after launching.
Example: Physics Application
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 expression for height. –16t2 + vt + s
–3600 + 3750 + 20
–16(15)2 + 250(15) + 20 Substitute 15 for t, 250 for v, and 20 for s. Simplify.
170The rocket is 170 ft high 15 seconds after launching.
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noyes
trinomial binomial
5 3
Determine whether each expression is a monomial.
1. 5a2z4 2. 3√x
Classify each expression as a monomial, a binomial, a trinomial, or not a polynomial.
3. 2x – 3x – 6 4. 3m3+ 4m
Find the degree of each polynomial.
5. 3a2 + a5 + 26 6. 2c3 – c2
Lesson Quiz
