Warm-Up 4 minutes Evaluate each expression for x = -2. 1) -x + 1 Simplify each expression. 4) (x + 5) + (2x + 3) 5) (x + 9) – (4x + 6) 6) (-x2 – 2) – (x2 – 2)

5.1 An Intro to Polynomials Objectives: Identify, evaluate, add, and subtract polynomials Classify polynomials, and describe the shapes of their graphs

Classification of a Polynomial Degree Name Example n = 0 constant 3 n = 1 linear 5x + 4 n = 2 quadratic 2x2 + 3x - 2 n = 3 cubic 5x3 + 3x2 – x + 9 n = 4 quartic 3x4 – 2x3 + 8x2 – 6x + 5 n = 5 quintic -2x5 + 3x4 – x3 + 3x2 – 2x + 6

Example 1 Classify each polynomial by degree and by number of terms. a) 5x + 2x3 – 2x2 cubic trinomial b) x5 – 4x3 – x5 + 3x2 + 4x3 quadratic monomial

Example 2 Add (5x2 + 3x + 4) + (3x2 + 5) = 8x2 + 3x + 9

Example 3 -3x4y3 + 6x3y3 – 6x2 + 5xy5 + 1 5x5 - 3x3y3 - 5xy5 5x5 Add (-3x4y3 + 6x3y3 – 6x2 + 5xy5 + 1) + (5x5 – 3x3y3 – 5xy5) -3x4y3 + 6x3y3 – 6x2 + 5xy5 + 1 5x5 - 3x3y3 - 5xy5 5x5 – 3x4y3 + 3x3y3 – 6x2 + 1

Example 4 Subtract. (2a4b + 5a3b2 – 4a2b3) – (4a4b + 2a3b2 – 4ab)

Example 5 If the cubic function C(x) = 3x3 – 15x + 15 gives the cost of manufacturing x units (in thousands) of a product, what is the cost to manufacture 10,000 units of the product? C(x) = 3x3 – 15x + 15 C(10) = 3(10)3 – 15(10) + 15 C(10) = 3000 – 150 + 15 C(10) = 2865 $2865