Question

Identify the leading coefficient, degree, and end behavior of f(x) = -2x^7 - 4x^4 + 5x^2 + 15?

Answer 1

http://imgur.com/M1FdOdm
Help would be greatly appreciate. :-)

Answer 2

The leading coefficient is the coefficient of the term with the greatest exponent.
The degree of the polynomial is the highest exponent of the variable.

Answer 3

@mathstudent55 - so the leading coefficient would -2x^7?
and the degree would be 7?

Answer 4

The leading coefficient would just be -2 and yes the degree would be 7.

Answer 5

@douglaswinslowcooper - Thanks a lot! :-)
would you happen to know how to figure out the end behavior?

Answer 6

Sure, imagine you go to large x, both positive and negative, then the
-2x^7 term dominates all the others.

For big x<0, -2x^7 is big>0 because (-1)^7 = -1
For big x>0, -2x^7 is big<0 because (+1)^7 = +1

Answer 7

Thanks!