WARM – UP 1. Find all of the real roots of the function:

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Presentation transcript:

WARM – UP 1. Find all of the real roots of the function: 2. Using LONG DIVISION, divide:

Daily Check Monday!!!

IRRATIONAL How do I find the x-intercepts of a polynomial equation that will not factor?

IRRATIONAL ROOTS This will occur when you get a polynomial after synthetic division that CANNOT be factored! But you MUST get it down to a quadratic! Quadratic Formula:

f(x) = x4 + 3x3 – 5x2 – 15x Find all the roots: Always look to see if a function will factor. This function WILL factor.

f(x) = x4 + 3x3 – 5x2 – 15x 1 3 -5 -15 -3 x = 0 , -3 1 3 -5 -15 -3 15 What if it doesn’t factor to begin with or you aren’t sure? Find a root to begin synthetic division using your calculator, and get it down to a quadratic! f(x) = x4 + 3x3 – 5x2 – 15x x = 0 , -3 1 3 -5 -15 -3 1 3 -5 -15 -3 15 1 -5

Find all of the roots of: g(x) = x4 + 2x3 – 5x2 – 4x + 6 (-3 and 1 using the calculator) Find all of the roots of: g(x) = x4 + 2x3 – 5x2 – 4x + 6 ANSWER: -3, 1, ,

Find all of the roots of: g(x) = 4x3 – 16x2 + 11x + 3 (3 using the calculator) Find all of the roots of: g(x) = 4x3 – 16x2 + 11x + 3 ANSWER: 3, ,

Find all of the roots of: g(x) = x3 – x2 – 11x + 3 (-3 using the calculator) Find all of the roots of: g(x) = x3 – x2 – 11x + 3 ANSWER: -3, ,

Homework!!