Question

which is the factor of the polynomial
P(x) = x^3 − 5x^2 − 4x + 20

A. x - 4
B. x + 5
C. x + 2
D. x - 20

Answer 1

A ?

Answer 2

You can factor it like this:
\[x^2(x - 5) - 4(x - 5)\]
And then break that down to
\[(x - 2)(x + 2)(x - 5)\]
So you were close but no.

Answer 3

okay i see how you did that now ... a little tricky

Answer 4

interesting - that can be done to most polynomials?

Answer 5

Kinda sorta not really.
It's an easy way to solve cubics (which can be pretty annoying to solve) when it actually works, but it doesn't always.

Answer 6

=/ is it possible to graph?

Answer 7

Yes this was done tricky, how do you do general?
If of odd order you know there's at least one real solution.
I know there's a general way of doing it but I never learned.
In my engineering day I used the general cubic equation solution.

Answer 8

It's always possible to graph! :D
Especially with graphing calculators and computers and stuff that do the dirty work for you.

Answer 9

i cant even bring a calculator into my tests ...

Answer 10

general method?

Answer 11

like that?

Answer 12

Yes there's a general method to solve cubic as quadratic but not as simple and I never memorized it but had it as reference for class and work. Most math manual have it but today with software like Mathematica can find exact roots for 3rd and 4th order. In my day I learned slide rules then calculators and computer(not home) generally Fortran language

Answer 13

do you know if my graph is correct?

Answer 14

According to answer previously given it looks correct
(-2,0) (2,0) (5,0)

Answer 15

The x^3 terms determines +- infinity