Bell Ringer The polynomials and share a common binomial factor. What factor do they share?

Rational Root TheoremNovember 4, 2015

Objective Students will learn how the Rational Root Theorem can help factor polynomials.

How can we use the Rational Root Theorem to check our answers?

Essential Question

284 steps to get to the top!!

L’arc de TriompheConstruction began in 1806 and completed in 1836 (ordered by Napoleon!)It cost 9.3 million French francs at the time, which was a huge amount of money then

Review What is the point of factoring?

How do you determine which method of factoring to use?

What is the rule for end behavior if the highest degree is even?

What is the rule for end behavior if the highest degree is odd

How do you determine the maximum number of turns?

Rational Root Theorem Allows you to find potential zeroes of any polynomial

You can always check your work with factoring by using this

Remember that the highest degree gives you the number of possible roots for each function

What are roots again???

Rational Root Theorem

p=factors of constant term q=factors of leading coefficient

𝑥2+2𝑥−3 Using the Rational Root Theorem, what are possible factors of this polynomial?

Possible factors: 3, -3, 1, -1

How do you find the actual factors?

±3±1,±1±1

2 𝑥3+4 𝑥2+8 Using the Rational Root Theorem, what are possible factors of this polynomial?

Which fractions are equivalent? 1/1 and 2/2, 2/1 and 4/2, 4/1 and 8/2 Possible factors: 1, -1, 2, -2, 4, -4, 8, -8

How do you find the actual factors?

±1±1,±1±2,±2±1,±2±2,±4±1,± 4±2,±8±1,±8±2

How can you use the Rational Root Theorem to your advantage? If you factor a polynomial, you can always check your work by using the Rational Root Theorem

Relative Maximum & Minimum

With quadratics, we identified whether or not the vertex was a maximum or minimum of the graph. With polynomials, you can identify the relative maximum and minimums by looking at sections of the graph. They are the turning points of the graph Where are the relative max/min of this graph?

Sketching Graphs of Polynomials

In order to sketch the graph of these polynomials…1. Determine the end behavior and maximum

number of turns.2. Factor the polynomial to find the zeroes. Plot

them.3. Plug in a number between each of the zeroes

to sketch the remainder of the graph.

Graph 1. Determine the end

behavior and maximum number of turns.

2. Factor the polynomial to find the zeroes. Plot them.

3. Plug in a number between each of the zeroes to sketch the remainder of the graph.

Volume The volume of a box is 70 in3. It can be modeled by the expression . Determine the box’s length, width, and height in terms of x, then tell the box’s exact dimensions.