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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.