Holt CA Course 1

12-1 Polynomials

Warm UpWarm Up

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California StandardsCalifornia Standards

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Holt CA Course 1

12-1 Polynomials

Warm UpIdentify 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

Holt CA Course 1

12-1 Polynomials

Preview of Algebra 1 Preparation for 10.0 Students add, subtract, multiply, and divide monomials and polynomials. Students solve multistep problems, including word problems, by using these techniques.Also covered: 7AF1.2

California Standards

Holt CA Course 1

12-1 Polynomials

Vocabulary

polynomialbinomialtrinomialdegree of a polynomial

Holt CA Course 1

12-1 Polynomials

Recall that a monomial is a number, variable, or a product of numbers and variables with exponents that are whole numbers.

Holt CA Course 1

12-1 Polynomials

monomial not a monomial

3 and 4 are whole numbers.

Additional Example 1: Identifying Monomials

Determine whether each expression is a monomial.

y does not have a exponent that is a whole number.

B. 3x3√yA. √2 • x3y4

Holt CA Course 1

12-1 Polynomials

Check It Out! 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.

Holt CA Course 1

12-1 Polynomials

A polynomial is one monomial or the sum or difference of monomials. A simplified polynomial can be classified by the number of monomials, or terms, that it contains. A monomial has 1 term, a binomial has 2 terms, and a trinomial has 3 terms.

Holt CA Course 1

12-1 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

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.

trinomial Polynomial with 3 terms.

binomial Polynomial with 2 terms.

Holt CA Course 1

12-1 Polynomials

Check It Out! Example 2

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

binomial Polynomial with 2 terms.

not a polynomial 2.5 is not a whole number.

monomial Polynomial with 1 term.

binomial Polynomial with 2 terms.

Holt CA Course 1

12-1 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 degree of the term with the greatest degree. A polynomial can be classified by its degree.

4x2 + 2x5 + xy + 5

Degree 2 Degree 5 Degree 2 Degree 0

Degree 5

Holt CA Course 1

12-1 Polynomials Additional Example 3: Classifying Polynomials by

Their Degrees

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.

Holt CA Course 1

12-1 Polynomials Check It Out! Example 3

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.

Holt CA Course 1

12-1 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 expression for height. –16t + vt + 40

–1600 + 2750 + 40

–16(10)2 + 275(10) + 40 Substitute 10 for t and 275 for v. Simplify.

1190

The rocket is 1190 ft high 10 seconds after launching.

Holt CA Course 1

12-1 PolynomialsCheck 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 + 20. 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 + 20

–3600 + 3750 + 20

–16(15)2 + 250(15) + 20 Substitute 15 for t and 250 for v. Simplify.

170

The rocket is 170 ft high 15 seconds after launching.

Holt CA Course 1

12-1 Polynomials

Lesson Quiz

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. 2x2 – 3x – 6 4. 3m3+ 4m

Find the degree of each polynomial.

5. 3a2 + a5 + 26 6. 2c3 – c2