Chapter Sections 3.6 & 3.7

Question 0

What is the factor theorem?

Answer 0

If the remainder is 0 after synthetic division then the (x-c) can be used in the factor form.

Question 1

What is the remainder theorem?

Answer 1

If there is a remainder after dividing by (x-c) then it is not a polynomial function
But if the remainder is zero then (x-c) then it is a polynomial

Question 2

Number of real roots theorem?

Answer 2

A polynomial of degree n, n is greater than or equal to 1, has at most n real zeros

Question 3

What are complex numbers

Answer 3

Imaginary and real numbers

Question 4

Square root of -1 is what

Answer 4

i

Question 5

i^2 is what? (Number)

Answer 5

-1

Question 6

What are conjugate pairs?

Answer 6

If a+bi is a solution to a polynomial then a-bi is a solution as well

Question 7

What do you do if you are given an imaginary zero for a polynomial?

Answer 7

You multiply the conjugate pairs and that becomes something you can divide the equation with in long division.

Question 8

How do you determine the vertex with an equation like f(x)=x^2-6x+9

Answer 8

To determine x you use h= (-b/2a)

Then to find y you use the answer to h (or the x coordinate) and plug it in to the f(x) equation and get the y coordinate

Question 9

How do you find the potential rational zeros?

Answer 9

List all the integers p (that are factors of the last number (a0))
Ex) 3 would have +/- 1, +/-3
Then list all the integers q for the leading coefficient
Ex) 2 would have +/-1, +/- 2
Then form all possible ratios of p/q
-You should have the same number of possibilities that the leading coefficient degree has.