Is negative 2x squared over y cubed a monomial? Is Negative pi a polynomial? ?

Question

If they are not why aren't they? In my algebra book it isn't very clear. They only give a few examples of what is and what isn't a monomial and polynomial.

Answer 1

You can string together variables with multiplication and it is still a monomial.  But if you do a division, it's not.  A monomial has to have all the variables with non-negative powers and possibly a coefficient (constant multiplier)

-2x is a monomial

y^3 is a monomial

-2x/y^3 is a division of two monomials.

-π is a monomial (just like 2, -3, ½), etc.  Here any variables would have an exponent of 0.

More examples of monomials:

0

-5

2.9

-1/π (tricky)

rst

r²s²t

5r²s²t

-5r²s²t

-5π r²s²t

Examples of things that *aren't* monomials

r^-1 (power must be non-negative, this is equivalent to 1/r)

r + s

r - s

r/s

r²s² + s