Question

What is the leading coefficient, degree, and end behavior `P(x)=-4x^2-3x^3+2x^2+4`?

Answer 1

Please see the explanation below:

Explanation:

`P(x)=-4x^2-3x^3+2x^2+4`
simplify and rewrite in standard form:
`P(x)=-3x^3-2x^2+4`

The leading coefficient is: `-3`

The degree of the polynomial is the highest power of any variable, so in this case we have a 3rd degree polynomial hence:
the degree = `3`

The end behavior of the graph of a function is determined by its degree and the sign of its leading coefficient, as follows:

1)Even power with positive leading coefficient: up on both ends.
2)Even power with negative leading coefficient: down on both ends.
3)Odd power with positive leading coefficient: down on left side , up on right side.
4)Odd power with negative leading coefficient: up on left side , down on right side.

So in this case #4 applies:
up on left side , down on right side