Unit 2 Algebra Investigations. Standards MM1A2. Students will simplify and operate with radical expressions, polynomials, and rational expressions. Add,

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Presentation transcript:

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: -4x 2 + x Standard Form: x 3 - 4x 2 + 3

You try. Write 9 – 3m 2 – m 3 + 2m in standard form. Answer: -m 3 –3m 2 + 2m + 9 Remember to order your exponents from greatest to least. Always separate your terms by a (+) or (-) sign.

Special names for polynomials: Polynomial# termsNamedegree 12 8x 4x x 3 + x 2 3x 2 – 4x+6 3x 4 -4x 3 +6x 2 -7

Example Using the vertical form to add and subtract polynomials. Add 12y 3 + y 2 – 8y + 3 and 6y 3 – 13y Adding and Subtracting Polynomials 12y 3 +y 2 –8y+3Align like terms and add. 6y 3 –13y+5 18y 3 +y 2 –21y+8 +

Use the vertical format to Subtract: (4x 2 +3x+2) – ( 2x 2 -3x+7) 4x 2 + 3x +2 - (2x 2 -3x +7) remember to add the opposite! x 2 + 6x - 5

Key Skills Use the horizontal form to add and subtract polynomials. Subtract 15x – 4 from 2x x. 9.1 Adding and Subtracting Polynomials 2x x – (15x – 4) = 2x x –15x + 4 Group like terms and subtract. = 2x 2 – 4x + 4

Example Find the difference. (-2x 3 + 5x 2 – x + 8) – (-2x 3 + 3x – 4) -2x 3 + 5x 2 – x x 3 – 3x x 3 + 2x 3 + 5x 2 – x – 3x x 2 – 4x + 12

Example Find the difference. (x 2 – 8) – (7x + 4x 2 ) x 2 – 8 – 7x – 4x 2 x 2 – 4x 2 – 7x – 8 -3x 2 – 7x - 8

Practice A. Find the sum: (3x 2 + 5x) + (4 – 6x – 2x 2 )B. Subtract: (3x 2 – 2x +3) – (x 2 + 2x – 4) Answers: x 2 – x + 4, 2x 2 – 4x + 7

Summarizer How do you determine the degree of a polynomial? Classify 3x 5 +4x 2 -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. 5 th degree, Trinomial

Homework Page 62 Number all