Unit 2

Algebra Investigations

Standards

MM1A2. Students will simplify and operate with radical expressions, polynomials, and rational expressions. Add, subtract, multiply and divide polynomials. Use area and volume models for polynomial arithmetic.

MM1G2. Students will understand and use the language of mathematical argument and justification. Use conjecture, inductive reasoning, deductive

reasoning, counterexamples, and indirect proof as appropriate.

Essential Question

Unit: In what ways can algebraic methods be used in problem solving?

Lesson: How do we use patterns to write algebraic

expressions to represent geometric and numerical patterns?

Definitions

Polynomial: monomial, or a sum or difference of monomials.

Degree of a polynomial: exponent with the greatest value within the polynomial

Standard form (of a polynomial): left to right, in descending order, greatest exponent to the least.

9.1 Adding and Subtracting Polynomials

Definitions

Monomial: one term polynomial Binomial: two term polynomial Trinomial: three term polynomial Use the word Polynomial to describe 4 or

more terms

Classifying Polynomials by Degree

Degree 0: CONSTANT Degree 1: Linear Degree 2: Quadratic Degree 3: Cubic Degree greater than 3: Called the nth degree.

Writing polynomials in standard form

Combine like terms Then write terms in order starting with the

highest exponent. The constants (#s without variables) come

last! Ex: -4x2 + x3 + 3 Standard Form: x3 - 4x2 + 3

You try.

Write 9 – 3m2 – m3 + 2m in standard form. Answer: -m3 –3m2 + 2m + 9

Remember to order your exponents from greatest to least. Always separate your terms by a (+) or (-) sign.

Special names for polynomials:

Polynomial # terms

Name degree

12

8x

4x2 + 3

5x3 + x2

3x2 – 4x+6

3x4-4x3+6x2-7

Example

Using the vertical form to add and subtract polynomials.

Add 12y3 + y2 – 8y + 3 and 6y3 – 13y + 5.

9.1 Adding and Subtracting Polynomials

12y3 + y2 – 8y + 3Align like terms andadd. 6y3 –13y + 5

18y3 + y2 –21y + 8

++

Use the vertical format to Subtract:

(4x2+3x+2) – ( 2x2-3x+7)

4x2 + 3x +2 - (2x2 -3x +7) remember to add the opposite!

--------------------------- 2x2 + 6x - 5

Key Skills

Use the horizontal form to add and subtract polynomials.

Subtract 15x – 4 from 2x2 + 11x.

9.1 Adding and Subtracting Polynomials

2x2 + 11x – (15x – 4)

= 2x2 + 11x –15x + 4

Group like terms andsubtract.

= 2x2 – 4x + 4

Example

Find the difference.

(-2x3 + 5x2 – x + 8) – (-2x3 + 3x – 4)

-2x3 + 5x2 – x + 8 + 2x3 – 3x + 4

-2x3 + 2x3 + 5x2 – x – 3x + 8 + 4

5x2 – 4x + 12

Example

Find the difference.

(x2 – 8) – (7x + 4x2)

x2 – 8 – 7x – 4x2

x2 – 4x2 – 7x – 8

-3x2 – 7x - 8

Practice

A.A.Find the sum: (3x2 + 5x) + (4 – 6x – 2x2)

B.B. Subtract: (3x2 – 2x +3) – (x2 + 2x – 4)

Answers: x2 – x + 4, 2x2 – 4x + 7

Summarizer

How do you determine the degree of a polynomial?

Classify 3x5+4x2-7 in two different ways. (What is it specifically called? What is the degree of the polynomial?)

Degree of a polynomial is the highest degree within.

5th degree, Trinomial

Homework

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