warm up 1.what is the absolute minimum of f(x) = 2x 4 – 17x 3 + 37x 2 – 7x – 15 2.a ball is...
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Warm Up1. What is the absolute minimum of
f(x) = 2x4 – 17x3 + 37x2 – 7x – 15
2. A ball is thrown into the air. It’s height above the ground in feet is given by h(t)= -16t2 + 75t + 300 where t is time in seconds. How long does it take before the ball hits the ground?
3. Divide without a calculator 15983 ÷ 4
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DividingPolynomials
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Review of long division…
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Review of long division…
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Remember all exponents must be accounted for and have a place holder when dividing…
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Review of synthetic division…
Remember the divisor must be in the form (x – k) to use this method.
In other words, the leading coefficient and the exponent on x must be 1.
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The Remainder Theorem…
Given f(x) = x4 – 10x2 – 2x + 4Find f(-3).
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The Factor Theorem…
What makes a number a “factor” of another number?
For example…why is 3 a factor of 12?
(x – k) is a factor of f(x) if and only if the remainder is 0 … f(k) = 0.
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Show that x = -4 is a solution to x3 – 28x – 48 = 0.Use this to completely factor f(x) = x3 – 28x – 48
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Show that x = -2 is a solution to x3 + 2x2 – 3x – 6 = 0.
Use this to completely factor f(x) = x3 + 2x2 – 3x – 6
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Use the graph to guess possible linear factors of f(x). Then completely factor f(x).
F(x) = 5x3 – 12x2 – 23x + 42
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Homework
page 223 – 224#3 – 24 (multiples of 3)
25 and 26