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

Answer:

• -1 — does not cross
• 0 — does not cross
• 2 — crosses

Step-by-step explanation:

P(x) = x^4(x -2)^3(x +1)^2 has zeros at ...

• -1 — multiplicity 2 (does not cross)
• 0 — multiplicity 4 (does not cross)
• 2 — multiplicity 3 (crosses)

The zeros that have even multiplicity are points where the graph does NOT cross the x-axis. This is true because an even power of a number does not change sign when the sign of the number changes.