Question

Will give a medal and a fan! A polynomial function can be written as (x - 2)(x - 3)(x + 5). What are the x-intercepts of the graph of this function? Please help :) Walk me through it if you can?

Answer 1

This is a cubic function because it will multiply out to be an x^3 polynomial. That means it will cross the x axis three times. Those sets of parenthesis above represent the places where x = 0, or in other words, where the graph goes through the x axis.

Answer 2

Set each set of parenthesis equal to 0, like this:
x - 2 = 0
x - 3 = 0
x + 5 = 0
and solve each of them for x. The first one says that x = 2. So that is one place where the graph goes through the x axis....at x = 2, or (2, 0).

Answer 3

The next one is x - 3 = 0. That one says that x = 3. That is another place where the graph goes through the x axis....at (3, 0).

Answer 4

The last one is x + 5, which tells us that x = -5. So the graph with the x intercepts from above looks something like this:

Answer 5

Those dark dots on the x axis are your intercepts we just found. Now, depending upon what the equation is, your graph might look something like this...