Pre-Algebra

13-1 Polynomials

Pre-Algebra HOMEWORK

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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

13-1 Polynomials

Pre-Algebra

Warm UpWarm Up

Lesson PresentationLesson Presentation

Problem of the DayProblem of the Day

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

Pre-Algebra

13-1 Polynomials

yes no yes

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

Vocabulary

monomialpolynomialbinomialtrinomialdegree of a polynomial

Insert Lesson Title Here

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.

Monomials 2n, x3, 4a4b3, 7

Not monomials p2.4, 2x, √x, g25

Pre-Algebra

13-1 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√y

Pre-Algebra

13-1 Polynomials

A. √2 • x3y4

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

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.

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

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.

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 + 2x5 + x + 5

Degree 2 Degree 5 Degree 1 Degree 0

Degree 5

Pre-Algebra

13-1 Polynomials

Additional Example 3A & 3B: 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.

Pre-Algebra

13-1 Polynomials

Try This: Example 3A & 3B

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.

Pre-Algebra

13-1 Polynomials

Additional Example 3C: 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.

Pre-Algebra

13-1 Polynomials

Try This: Example 3C

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.

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 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.

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 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.

170

The rocket is 170 ft high 15 seconds after launching.

Pre-Algebra

13-1 Polynomials

Lesson Quiz

noyes

Insert Lesson Title Here

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

Pre-Algebra

13-1 Polynomials