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7-5 Polynomials
Warm Up
Evaluate each expression for the given value
of x.
1. 2x + 3; x = 2 7
3. –4x – 2; x = –1 2
2. x2 + 4; x = –3 13
4. 7x2 + 2x = 3 69
Identify the coefficient in each term.
5. 4x3 4
6. y3 1
7. 2n7 2
Holt Algebra 1
8. –54 –1
7-5 Polynomials
Graph the line with the given the slope and
y-intercept.
y intercept = 4
RISE 2


RUN
5
y
2
5
Holt Algebra 1
x
7-5 Polynomials
Scientific notation is a method of writing
numbers that are very large or very small. A
number written in scientific notation has two
parts that are multiplied.
The first part is a number that is greater than or equal
to 1 and less than 10.
The second part is a power of 10.
Holt Algebra 1
7-5 Polynomials
Learning Targets
Students will be able to: Classify
polynomials and write polynomials in
standard form. Evaluate polynomial
expressions.
Holt Algebra 1
7-5 Polynomials
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.
Holt Algebra 1
7-5 Polynomials
Find the degree of each monomial.
D. 1.5k2m
A. 4p4q3
7
B. 7ed
2
C. 3
0
3
E. 4x
1
F. 2c3
3
The degree of a monomial is the sum of the
exponents of the variables. A constant has degree 0.
Holt Algebra 1
7-5 Polynomials
Remember!
The terms of an expression are the parts being
added or subtracted. See Lesson 1-7.
Holt Algebra 1
7-5 Polynomials
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.
Holt Algebra 1
7-5 Polynomials
Find the degree of each polynomial.
A. 11x7 + 3x3
7
D. x3y2 + x2y3 – x4 + 2
5
B.
4
C. 5x – 6
1
The degree of a polynomial is the degree
of the term with the greatest degree.
Holt Algebra 1
7-5 Polynomials
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.
Holt Algebra 1
7-5 Polynomials
Write the polynomial in standard form. Then
give the leading coefficient.
6x – 7x5 + 4x2 + 9
Degree
1
5
2
0
–7x5 + 4x2 + 6x + 9
5
2
1
The leading coefficient is  7.
Holt Algebra 1
0
7-5 Polynomials
Remember!
A variable written without a coefficient has a
coefficient of 1.
y5 = 1y5
Holt Algebra 1
7-5 Polynomials
Write the polynomial in standard form. Then
give the leading coefficient.
y2 + y6 – 3y
Degree
2
6
1
y6 + y2 – 3y
6
2
1
The leading coefficient is 1.
Holt Algebra 1
7-5 Polynomials
Write the polynomial in standard form. Then
give the leading coefficient.
16 – 4x2 + x5 + 9x3
Degree 0
2
5
3
x5 + 9x3 – 4x2 + 16
5
3
The leading coefficient is 1.
Holt Algebra 1
2
0
7-5 Polynomials
Write the polynomial in standard form. Then
give the leading coefficient.
18y5 – 3y8 + 14y
Degree
5
8
1
–3y8 + 18y5 + 14y
8
5
The leading coefficient is  3.
Holt Algebra 1
1
7-5 Polynomials
Some polynomials have special names based on
their degree and the number of terms they have.
Degree
Name
Terms
Name
0
Constant
1
Monomial
1
Linear
2
Binomial
2
Quadratic
Trinomial
3
4
Cubic
Quartic
3
4 or
more
5
Quintic
6 or more
Holt Algebra 1
6th,7th,degree
and so on
Polynomial
Problem 1
Problem 2
7-5 Polynomials
Classify each polynomial according to its
degree and number of terms.
A. 5n3 + 4n
Degree 3 Terms 2
cubic binomial
B. 4y6 – 5y3 + 2y – 9 4y6 – 5y3 + 2y – 9 is a
Degree 6 Terms 4
6th-degree polynomial
C. –2x
Degree 1 Terms 1
linear monomial.
Tables
Holt Algebra 1
7-5 Polynomials
Classify each polynomial according to its
degree and number of terms.
a. x3 + x2 – x + 2
Degree 3 Terms 4
cubic polynomial
b. 6
Degree 0 Terms 1
constant monomial
c. –3y8 + 18y5 + 14y
Degree 8 Terms 3
8th-degree trinomial
Tables
Holt Algebra 1
7-5 Polynomials
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?
–16t2 + 220
–16(3)2 + 220
–16(9) + 220
–144 + 220
76 feet
HW pp.HW:
479-481/18-78
Even,81-89
p. 479/18-72 EVEN
Holt Algebra 1