Question

Lots and lots of questions.
For this equation
x^3+3x^2-18x/x^2-x-6
how would I find

A. The Domain
B. Holes
C. X and Y intercepts.

Miscellaneous question as well.
How do you find real roots and complex roots?

Answer 1

\[\frac{x(x+6)(x-3)}{(x-3)(x+2)}\]

Answer 2

Domain, real numbers not equal to -2, 3
x intercept found by letting y = 0 So x intercepts are 0, -6, 3
Of course the roots are the x intercepts.
y intercept found by letting x = 0. So y intercept is 0

Answer 3

There is a hole at x = 3 and a vertical asymptote at x = -2

Answer 4

Find the real roots by factoring or using the quadratic formula.

Answer 5

Same for the complex roots.

Answer 6

OK so you factor both numerator and denominator then.... ????

What process do you use to get the domain?

Answer 7

Eliminate the numbers that cause the fraction to be undefined. Or in other words, eliminate the numbers that cause the denominator to be 0