Question

The function p(x) is an odd degree polynomial with a negative leading coefficient. If q(x) = x3 + 5x2 - 9x - 45, which statement is true? A. As x approaches negative infinity, p(x) approaches positive infinity and q(x) approaches negative infinity. B. As x approaches negative infinity, p(x) and q(x) approach positive infinity. C. As x approaches negative infinity, p(x) and q(x) approach negative infinity. D. As x approaches negative infinity, p(x) approaches negative infinity and q(x) approaches positive infinity.

Answer 1

As x approaches negative infinity, p(x) approaches positive infinity and q(x) approaches negative infinity.

Explanation:

The order of the polynomial and the sign of the leading coefficient will let us find the correct answer easily,

If you get a negative number (such as negative infinity) and you take it to an odd power, (for example 3), you will still get a negative number.

As q(x) has a positive leading coefficient, this means that as x approaches negative infinity, q(x) will approach too negative infinity.

Since p(x) has an odd degree, but negative leading coefficient,

(-)*(-) = +

And this means that p(x) approaches positive infinity