Question

Consider P(x) = x4(x − 2)3(x + 1)2. For each zero, determine if the graph crosses the x-axis. How do you know?

Answer 1

To find zeros of this polynomial, set the poly = to zero and solve the resulting equation for x.

Please clarify this: does your "x4" mean x^4 (x to the 4th power), or something else?

Very important: for clarity use the symbol " ^ " to indicate exponentiation.

My educated guess is that by "P(x) = x4(x − 2)3(x + 1)2" you actually meant

P(x) = x^4(x − 2)^3(x + 1)^2, which is a 6th order polynomial.

Set this equal to zero and attempt to solve the resulting equation for x. You should expect to find up to six zeros (or solutions).

Answer 2

B) The zeros at 0 and −1 do not cross the x-axis because they have even multiplicity. The zero at 2 crosses the x-axis because it has odd multiplicity.

Explanation:

The multiplicity of the zero determines whether the graph crosses the x-axis at that zero. If the multiplicity is even, the graph does not cross. If the multiplicity is odd, the graph crosses.