Question

h(x)=2x^3+5x^2-31x-15
List all the possible zeros.

I'm confused as to which side is p and which is q...

Answer 1

list all the numbers where the numerator divides 15 and the denominator divides 2
it is a pretty big list
don't forget the \(\pm\)

Answer 2

got it or no?

Answer 3

Yhu mean the factors right?

Answer 4

Right, all the possible real zeros of the function are the numbers made by dividing the factors of 15 by the factors of 2. So all the possibilities would look something like this:
\[\frac{ \pm 15, 5, 3, 1 }{ \pm 2, 1 }\] So picking any number on top (plus or minus) and dividing it by any number on bottom (plus or minus) will be a possible real zero. From there, it you're often guessing and checking to see what works.

Answer 5

yeah factors
like
\[\pm1,\pm3,\pm15\] for starters

Answer 6

That would mean that p is the leading coefficient and the constant is q right?

Answer 7

then
\[\pm\frac{1}{2},\pm\frac{3}{2},\pm\frac{5}{2},\pm\frac{15}{2}\]

Answer 8

If you're used to it in terms of p and q, then yes, it'd be factors of q divided by factors of p.

Answer 9

i missed \(\pm5\)

Answer 10

it is easier to forget about p and q and just write it
all fractions where the numerator of the fraction divides the constant and the denominator of the fraction divides the leading coefficient

Answer 11

like if you had the line
\[2x-3=0\] it would be \(\frac{3}{2}\)

Answer 12

:o So it's.... q over p --> q/p
Not... p/q?

My teacher will mark me down if I don't. Her grading system is retarded and.... Yea.

Answer 13

it is usually written
\[\frac{p}{q}\] where \(p\) divides the constant and \(q\) divides the leading coefficient

Answer 14

p and q are variables, it makes no difference what you call them

Answer 15

so yeah, retarded is the word, if she thinks it makes a difference how you write it, she is not that bright

Answer 16

As long as you know that it's factors of the constant term divided by factors of the leading coefficient, there is no problem, whatever you call them.

And to be fair, I get marked off every time I don't use the exact notation my professors use in my math classes, satellite, so I understand that sometimes teachers are just that way :/

Answer 17

they have to keep themselves employed, so i understand it too
that is why it take years to unlearn assumptions about what a variable is

Answer 18

My abstract algebra professor just says: "It's international notation, you don't get to change it when you feel like it."

Answer 19

tell her it is
\[\frac{\heartsuit}{\clubsuit}\] where \(\heartsuit\) divides the constant and \(\clubsuit\) divides the leading coefficient

Answer 20

^

Answer 21

the originators of variables used colors

Answer 22

international my foot
\[\mathbb{Z}_p\] may be international, or \(\mathbb{R}\) but you can call the elements of your group \(x, g, a, \) whatever

Answer 23

Sorry, my computer crashed...
@satellite73 were the fractions yhu listed above the full answer or part? Cuz I have an answer, but if that was the answer, then I messed up somewhere.