Answer:
C ( x = 2 (multiplicity of 2), x = -2, x = -4)
A ( x = 5 (crosses), x = -3 (touches))
Step-by-step explanation:
Here are a couple of rules that helped me come to these answers.
1. When finding a zero, you flip the value inside of the parenthesis. For example (x + 2) would have the zero of x = -2.
2.The multiplicity of something is how many times the same zero is there. It is the exponent outside of the equation. For the first question, the (x - 2) has an exponent of 2, thus it has the multiplicity of 2.
3. The multiplicity determines whether the line just touches (or "bounces" off) the x axis or crosses the x axis. If the multiplicity is odd, it crosses the axis. If the multiplicity is even, it just touches the axis. A good way to remember this is with linear and quadratic equations. A linear is commonly know as only having an exponent of 1 (an odd) number and would cross the x axis. A quadratic equation has an exponent of two (an even number) so the line "bounces" on a graph.
