13-1 Polynomials
Pre-Algebra HOMEWORK
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Pre-Algebra
13-1 Polynomials
Our Learning Goal
Students will be able
to classify, simplify,
add and subtract
polynomials.
Pre-Algebra
13-1 Polynomials
Students will be able to classify, simplify, add
and subtract polynomials by completing the
following assignments.
• Learn to classify polynomials by degree and
by the number of terms.
• Learn to simplify polynomials.
• Learn to add polynomials.
• Learn to subtract polynomials.
…..and that’s all folks!
Pre-Algebra
13-1 Polynomials
Today’s Learning Goal Assignment
Learn to classify
polynomials by
degree and by the
number of terms.
Pre-Algebra
13-1 Polynomials
Warm Up
Problem of the Day
Lesson Presentation
Pre-Algebra
13-1 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
Pre-Algebra
13-1 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
Pre-Algebra
13-1 Polynomials
Learn to classify polynomials by degree
and by the number of terms.
Pre-Algebra
13-1 Polynomials
Insert Lesson Title Here
Vocabulary
monomial
polynomial
binomial
trinomial
degree of a polynomial
Pre-Algebra
13-1 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.
Pre-Algebra
Monomials
2n, x3, 4a4b3, 7
Not monomials
p2.4,
2x,
5
√x, g2
13-1 Polynomials
Additional Example 1: Identifying Monomials
Determine whether each expression is a
monomial.
A. √2
•
x3y4
monomial
3 and 4 are whole
numbers.
Pre-Algebra
B. 3x3√y
not a monomial
y does not have a
exponent that is a whole
number.
13-1 Polynomials
Try This: Example 1
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.
Pre-Algebra
13-1 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
term, and a trinomial has 3 terms.
Pre-Algebra
13-1 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.
Pre-Algebra
13-1 Polynomials
Try This: 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.
Pre-Algebra
13-1 Polynomials
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
Degree 2
+
2x5
+
Degree 5
x
Degree 1
Degree 5
Pre-Algebra
+
5
Degree 0
13-1 Polynomials
Additional Example 3A & 3B: 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.
Pre-Algebra
13-1 Polynomials
Try This: Example 3A & 3B
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.
Pre-Algebra
13-1 Polynomials
Additional Example 3C: Classifying
Polynomials by Their Degrees
Find the degree of the polynomial.
C. –3x4 + 8x5 – 4x6
–3x4
Degree 4
+
8x5
Degree 5
–
4x6
Degree 6
The degree of –3x4 + 8x5 – 4x6 is 6.
Pre-Algebra
13-1 Polynomials
Try This: Example 3C
Find the degree of each polynomial.
C. –6x4 – 9x8 + x2
–6x4
Degree 4
–
9x8
Degree 8
+
x2
Degree 2
The degree of –6x4 – 9x8 + x2 is 8.
Pre-Algebra
13-1 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 + s. 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.
Pre-Algebra
13-1 Polynomials
Try This: 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.
Pre-Algebra
13-1 Polynomials
Insert Lesson Title Here
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. 2x – 3x – 6
4. 3m3+ 4m
trinomial
binomial
Find the degree of each polynomial.
5. 3a2 + a5 + 26 5
Pre-Algebra
6. 2c3 – c2 3