Answer:
As x tends to +∞, P tends to 0 and as x tends to -∞, P tends to 0.
Step-by-step explanation:
Let [tex]f(x) = ax^{2} + bx + c[/tex] and [tex]g(x) = - dx^{3} + ex^{2} + fx + g[/tex], where a, b, c, d, e, f, g all are positive coefficients.
So, the function f(x) has degree two and positive leading coefficient and g(x) has degree three and negative leading coefficient.
Now, let [tex]P = f(x) + g(x) = - dx^{3} + (a + e)x^{2} + (b + f)x + (c + g)[/tex]
Therefore, as x tends to +∞, P tends to 0 and as x tends to -∞, P tends to 0. (Answer)
