Warm-Up 5 minutes Simplify. 1) (x2)(x4) x6 2) (3x3y5)(12xy-2) 36x4y3 _____ 3y2

More on Polynomials Objectives: SWBAT To write polynomials in ascending and descending order To evaluate polynomials Why? So you can apply these principles to real-world situations. Mastery is 80% or better on 5 min checks and Indy work.

Example 1 Arrange each polynomial in descending order for the variable x. a) 3x + 3 + 4x7 – 4x6 = 4x7 – 4x6 + 3x + 3 b) 7xy2 +5x3y3 – 3x2y = 5x3y3 – 3x2y + 7xy2

Example 2 Collect like terms and arrange in descending order for the variable x. 4xy3 – 3x5y4 + 2xy3 + 4 = -3x5y4 + 6xy3 + 4

Practice Collect like terms and arrange in descending order for the variable x. 1) 3x2 – 2x + 3 – 5x2 – 1 - x 2) -4x2y + xy – 2x2y – xy + 3x3y

Example 3 Evaluate each polynomial for the given value. a) x2 + x + 1 for x = 3 = 32 + 3 + 1 = 9 + 3 + 1 = 13 b) 3x3 + 2x2 + 5 for x = 2 = 3(2)3 + 2(2)2 + 5 = 24 + 8 + 5 = 37

Practice Evaluate each polynomial for the given value. 1) -4x – 7 for x = 3 -19 2) -5x2 + 7x + 10 for x = 3 -14 3) 2x2y + 5xy – 4 for x = -4 and y = 5 56

Example 4 If a rock is thrown upward at a speed of 80 ft per second, the height it reaches in t seconds is 80t – 16t2. Find the height of the rock after 1 second, 2 seconds, and 4 seconds. 1 second 2 seconds 4 seconds 80t - 16t2 80t - 16t2 80t - 16t2 = 80(1) – 16(1)2 = 80(2) – 16(2)2 = 80(4) – 16(4)2 = 80 - 16 = 160 - 64 = 320 - 256 = 64 ft = 96 ft = 64 ft

Practice The lung capacity in liters for a woman can be estimated by the polynomial 0.041h – 0.018A – 2.69 (height (h) in centimeters; age (A) in years) Find the lung capacity for a 25 year-old woman who is 170cm tall. 0.041(170) - 0.018(25) -2.69 6.97 - .45 – 2.69 3.83 LITERS IS THE LUNG CAP OF A 25 YR OLD WOMAN 170CM TALL How will age and height change the outcomes?

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