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

DividingPolynomials

Review of long division…

Review of long division…

Remember all exponents must be accounted for and have a place holder when dividing…

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.

The Remainder Theorem…

Given f(x) = x4 – 10x2 – 2x + 4Find f(-3).

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.

Show that x = -4 is a solution to x3 – 28x – 48 = 0.Use this to completely factor f(x) = x3 – 28x – 48

Show that x = -2 is a solution to x3 + 2x2 – 3x – 6 = 0.

Use this to completely factor f(x) = x3 + 2x2 – 3x – 6

Use the graph to guess possible linear factors of f(x). Then completely factor f(x).

F(x) = 5x3 – 12x2 – 23x + 42

Homework

page 223 – 224#3 – 24 (multiples of 3)

25 and 26