M3D14 Have out: Bellwork: pencil, red pen, highlighter, GP notebook

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M3D14 Have out: Bellwork: pencil, red pen, highlighter, GP notebook 1. Find the zeros of P(x) = x3 – 4x2 + 2x – 8 and sketch y = P(x). 2. Is (x + 2) a factor of x4 – 13x2 +36 ? total:

1. Find the zeros of P(x) = x3 – 4x2 + 2x – 8 and sketch y = P(x). +1 (4,0) +1 +1 +1 +1 (0, –8) +1 graph +1 +1 +1 End behavior: Be sure to put an inflection point somewhere. +2 +1

Yes it is! 2) Is (x + 2) a factor of x4 – 13x2 +36 ? we need to factor to find out: 36 x4 – 13x2 +36 –9 –4 (x2 – 4)(x2 – 9) +1 –13 (x – 2)(x + 2)(x – 3)(x + 3) +4 Yes it is! +1 total:

Long Division of polynomials Recall how to divide numbers Example #1: 126 ÷ 5 = divisor 5 = __________ 126 ___ dividend 25 quotient – remainder 1 – remainder Since there is a ___________, 5 is not a ______ of 126. factor

Example #2: Let P(x) = x2 + 3x + 2 and d(x) = x +1 x+ 2 Therefore, q(x) = _______ P(x) = ________ and the _________ = 0 because d(x) is a _______ of P(x). remainder factor

Example #3: Let P(x) = x3 – 4x2 – 7x + 10 and and d(x) = x – 1, find . Use the distributive property. Go over your signs in a different color! – (_____)(__________) x – 1 x2 – 3x – 10 + (_____)(_____)(_____) x – 1 x – 5 x + 2 + – -10 -5 2 -3

+ + Example #4: Let P(x) = 2x3 – 3x2 – 10x + 11 and d(x) = x + 2, find . quotient q(x) _____________ – – dividend P(x) _____________ divisor d(x) _____________ + + – – Since r(x) ≠ 0, then x + 2 is _____ a factor of P(x). NOT remainder r(x) _____________

Or, the answer can be written as: Division Algorithm Example Or, the answer can be written as:

Example #5: Let P(x) = 2x4 – 3x3 + 2x – 5 and d(x) = x + 1, find .  We must include ___ coefficient placeholders for _______ terms. missing – – + + – – + +

Are there any missing terms in P(x)? Exercise #6: Let P(x) = x4 + 3x2 + x – 5 and d(x) = x2 – x + 2, find . Are there any missing terms in P(x)? – – + – + _ – + –

Are there any missing terms in P(x)? Exercise #7: Let P(x) = x4 + 5x3 + 3x – 2, and d(x) = x2 – 5, find . Are there any missing terms in P(x)? _ – + Work on the practice. _ – + _ – +

Complete the rest of the worksheets. Check your answers: Complete the rest of the worksheets.

Finish the worksheets