Question

10. What is the multiple zero and multiplicity of f(x) = (x - 3)(x - 3)(x + 5)?

Multiple zero is -3; multiplicity is 2
Multiple zero is 5; multiplicity is 1
Multiple zero is -5; multiplicity is 1
Multiple zero is 3; multiplicity is 2

Answer 1

D. Multiple zero is 3; multiplicity is 2

Explanation:

f(x) = (x-3)(x-3)(x+5)

0 = (x-3)(x-3)(x+5)

x = -5,3,3

notice 3 shows up twice. That would be your answer...So D.

Answer 2

Multiple zero is 3; multiplicity is 2

Explanation:

f(x) = (x - 3)(x - 3)(x + 5)

Rewriting

f(x) = (x - 3)^2(x + 5)

Setting equal to zero

0 = (x - 3)^2(x + 5)

Using the zero product property

(x-3)^2 = 0 x+5 = 0

x-3 = 0 x= -5

x=3 x-5

Since x-3 was squared, the multiplicity is 2