DO NOW : Simplify 1. -9b + 8b 2. 6y – y 3. 4m + (7 - m)

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Presentation transcript:

DO NOW : Simplify 1. -9b + 8b 2. 6y – y 3. 4m + (7 - m) 4. c – (3c + 1) 5. (3r + 4) + (-2r + 8) 6. (-2g + 1) – (2g + 1) 7. (5j – 7k) – ( 4j – 6k) Answers: -b, 5y, 3m + 7, -2c-1, r+12, -4g, j-k

Adding & Subtracting Polynomials

Essential Question How do I classify polynomials? How do I add and subtract polynomials?

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.

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 4: 4th Degree 5: 5th Degree 6 or higher: nth degree, where n is the 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: Remember to order your exponents from greatest to least. Always separate your terms by a (+) or (-) sign.

Special names for polynomials: # terms Name degree 12 1 Monomial 8x 4x2 + 3 2 Binomial 5x3 + x2 3 3x2 – 4x+6 Trinomial 3x4-4x3+6x2-7 4 polynomial

Example 1 (3x2 +4x-2) + (5x2 - 6x - 8) Group like terms and subtract.

Example 2 Subtract 15x – 4 from 2x2 + 11x. Distribute the negative Group like terms and subtract. 2x2 + 11x – (15x – 4) = 2x2 + 11x –15x + 4 = 2x2 – 4x + 4

Example 3 Find the difference. (-2x3 + 5x2 – x + 8) – (-2x3 + 3x – 4)

Example 5 Using the vertical form to add and subtract polynomials. Add 12y3 + y2 – 8y + 3 and 6y3 – 13y + 5. Align like terms and add. 12y3 + y2 – 8y + 3 + 6y3 – 13y + 5 18y3 + y2 – 21y + 8

Use the vertical format to Subtract: (4x2+3x+2) – ( 2x2-3x+7) 4x2 + 3x +2 4x2 + 3x +2 - (2x2 -3x +7) -2x2 +3x -7 --------------------------- + 2x2 + 6x - 5

Example 6 Find the difference. (x2 – 8) – (7x + 4x2)

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

Classwork Homework In textbook: p. 61 # 7 – 12 and p. 62 # 4 – 9 Adding and Subtracting Wkst & Did You Hear Wkst Homework In textbook: p. 61 # 7 – 12 and p. 62 # 4 – 9