What is the the degree of polynomial P defined by : P(x) = -5(x - 2)(x^3 + 5) + x^5?

To find the degree of the polynomial P(x) = -5(x - 2)(x^3
+ 5) + x^5.

The degree of the polynomial is the degree of
the highest term.

So we expand the right
side:

P(x) = -5(x-2)(x^3+5)
+x^5

P(x) = -5(x^4
+5x-2x^3-10)+x^5.

P(x) = -5(x^4-2x^3+5x-10)
+x^5.

P(x) =
-5x^4+10x^3-25x+50+x^5.

We arrange the terms on the right
side.

P(x) = x^5 -5x^4
+10x^3-25x+50

The highest term is x^5 with degree
5.

So the degree of the polynomial is
5.