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

2. Daily Check Monday!!!

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

4. 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:

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

6. 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

7. 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, ,

8. 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, ,

9. 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, ,

10. Homework!!