Question

40 Points!!!!!!!!!!

For the polynomial, list each real zero and its multiplicity. Determine whether the graph
crosses or touches the x-axis at each x -intercept.
f(x) = 3(x + 7)(x + 3)^2?
A? B? C? D?

Answer 1

B

Explanation:

You find the multiplicity by looking at the power of the original root. You can imagine it as
`(x+7)^1(x+3)^2`. Now set those equal to 0 to find the value of them as roots.

`x+7=0\\x+3=0`

Solve them both and you get:

`x=-7\\x=-3`

Now as we saw in the origin of the roots above that (x + 7) was raised to the first power. That means it has a multiplicity of one, which also means it crosses when it reaches the x-axis. (x + 3) however had a multiplicity of 2, since it was squared. That means that (x + 3) will touch and turn the x-axis.

Therefore the answer is B since that agrees with everything we said.