Checkpoint: Multiplicity Solution

Write the polynomial equation given the graph.

$a < 0, n = odd degree n = 1 + 3 + 2 + 1 = 7 - a (x - (- 5)) {(x - (- 4))}^{3} {(x - (- 2))}^{2} (x - 0) = 0 - a x {(x + 4)}^{3} {(x + 2)}^{2} (x + 5) = 0$

Note

Q: Why is it important to determine if the root is a cross-through, bounce, or snake?
A: Because those descriptions determine the multiplicities.

Q: Why does the variable “a” need to be included in your answer?

A: Because “a” represents the leading coefficient which determines the end behavior.