Holt Algebra 1

7-5 Polynomials

Warm UpEvaluate each expression for the given value of x.

1. 2x + 3; x = 2 2. x2 + 4; x = –3

3. –4x – 2; x = –1 4. 7x2 + 2x = 3

Identify the coefficient in each term.

5. 4x3 6. y3

7. 2n7 8. –54

7 13

2 69

4 1

2 –1

Holt Algebra 1

7-5 Polynomials

Graph the line with the given the slope and y-intercept.

y intercept = 4

x

y2

5

RISE

RUN

25

Holt Algebra 1

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

Students will be able to: Classify polynomials and write polynomials in standard form. Evaluate polynomial expressions.

Learning Targets

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.

A. 4p4q3

7

B. 7ed

2

C. 3

0

The degree of a monomial is the sum of the exponents of the variables. A constant has degree 0.

D. 1.5k2m

3

E. 4x

1

F. 2c3

3

Holt Algebra 1

7-5 Polynomials

The terms of an expression are the parts being added or subtracted. See Lesson 1-7.

Remember!

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

B.

4

The degree of a polynomial is the degree of the term with the greatest degree.

C. 5x – 6

1

D. x3y2 + x2y3 – x4 + 2

5

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 –7x5 + 4x2 + 6x + 9

Degree 1 5 2 0 5 2 1 0

The leading coefficient is .7

Holt Algebra 1

7-5 Polynomials

A variable written without a coefficient has a coefficient of 1.

Remember!

y5 = 1y5

Holt Algebra 1

7-5 Polynomials

Write the polynomial in standard form. Then give the leading coefficient.

y2 + y6 – 3y y6 + y2 – 3y

Degree 2 6 1 2 16

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 x5 + 9x3 – 4x2 + 16

Degree 0 2 5 3 0235

The leading coefficient is 1.

Holt Algebra 1

7-5 Polynomials

Write the polynomial in standard form. Then give the leading coefficient.

18y5 – 3y8 + 14y –3y8 + 18y5 + 14y

Degree 5 8 1 8 5 1

The leading coefficient is .3

Holt Algebra 1

7-5 Polynomials

Some polynomials have special names based on their degree and the number of terms they have.

Degree Name

0

1

2

Constant

Linear

Quadratic

3

4

5

6 or more 6th,7th,degree and so on

Cubic

Quartic

Quintic

NameTerms

Monomial

Binomial

Trinomial

Polynomial4 or more

1

2

3

Problem 1

Problem 2

Holt Algebra 1

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

Degree 6 Terms 4

4y6 – 5y3 + 2y – 9 is a

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 + 2Degree 3 Terms 4 cubic polynomial

b. 6

Degree 0 Terms 1 constant monomial

c. –3y8 + 18y5 + 14yDegree 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 + 22076 feet

HW pp. 479-481/18-78 Even,81-89HW: p. 479/18-72 EVEN