1. Adding & Subtracting Polynomials Lesson 10.1

2. 43210 In addition to level 3.0 and above and beyond what was taught in class, the student may: · Make connection with other concepts in math · Make connection with other content areas. The student will be able to use properties of rational and irrational numbers to write, simplify, and interpret expressions on contextual situations. - justify the sums and products of rational and irrational numbers -interpret expressions within the context of a problem The student will be able to use properties of rational and irrational numbers to write and simplify expres sions based on contextual situations. -identify parts of an expression as related to the context and to each part With help from the teacher, the student has partial success with real number expressions. Even with help, the student has no success with real number expressions. Learning Goal 1 (HS.N-RN.B3 and HS.A-SSE.A.1): The student will be able to use properties of rational and irrational numbers to write, simplify, and interpret expressions based on contextual situations.

3. Polynomial: Poly: Manynomial: terms Form:ax k Where k is a non-negative integer. This is a polynomial in one variable. k is the degree of ax. ax alone has a degree of 1 The constant “a” has a degree of 0.

4. Degree: the degree of a polynomial is the largest degree of its terms. Standard form: terms are written in descending order from the largest to the smallest degree. Coefficient: the integer in front of the variable. How many you have of each variable. If no number, you have one.

5. Put this in standard form. -4x 2 + 3x 3 + 2 3x 3 – 4x 2 + 2 Name the coefficients and degree. 2x 3 + (-1)x 2 + 5 -5x 2 + 10x - 3 Coefficients: 2, -1 Degree: 3 Coefficients: -5, 10 Degree: 2

6. Classifying Polynomials PolynomialPolynomial Degree Classify Polynomial Terms 60Mononomial -2x1Mononomial 3x+11Binomial -x 2 +2x-52Trinomial 4x 3 -8x3Binomial 2x 4 -7x 3 -5x+14Polynomial

7. Adding Polynomials : add like terms ! You add the coefficients, not the variables! (2x 2 +x-5) + (x 2 +x+6) remove ( ) = 2x 2 +x 2 +x+x-5+6 =3x 2 +2x+1 Horizontal format:

8. Vertical format: line up like terms and add. (2x 2 +x-5) + (x 2 +x+6) remove ( ) and line up like terms. 2x 2 +x-5 + x 2 +x+6 3x 2 +2x+1

9. Subtracting polynomials: use either vertical or horizontal format. ***Remember to change the signs of every term in the second polynomial when you remove the ( )! Vertical format: (8x 4 -3x 2 -11x-3) – (-13x 4 -3x 2 +2x-17) 8x 4 - 3x 2 - 11x - 3 13x 4 +3x 2 -2x+17 (combine after changing signs) 21x 4 -13x+14

10. Horizontal format: (8x 4 -3x 2 -11x-3) – (-13x 4 -3x 2 +2x-17) Remove ( ) changing the signs in the second polynomial. You are adding the opposites! 8x 4 -3x 2 -11x-3 + 13x 4 +3x 2 -2x+17 ( now combine like terms ) 21x 4 -13x+14 Classify this by degree and terms. 4, trinomial

11. Find the area of the shaded region. x 2x 4 x 2 - = A= bh-bh = x  2x – 4  = 2x 2 – 2x