Question

For f(x)=(x+2)^4(x-3), 2 is a zero of multiplicity 4. True or False. If false why?

Answer 1

well to find the zeros you need to solve

x + 2 = 0

and

x - 3 = 0

multiplicity means that the (x + 2) is raised to the power 4...

its like saying

(x+2)(x+2)(x+2)(x+2)(x-3)

hope this helps

Answer 2

so then I would have to foil them out. then use synthetic division? i know the answer already, but i was wondering if there were an easier way?

Answer 3

i just realized the answer is in the question and that means it's -2

right off the back

Answer 4

nope... all you need to do is solve

x + 2 =0

x - 3 = 0

and then decide is x = 2 is a zero of of multiplicity 4

is you have a quaratic

f(x) = (x + 3)(x - 5) the zeros are when x + 3 = 0 which is x = -3

and when x - 5 = 0 which is x = 5

so apply the same reasoning...

(x + 2)^4 means its a repeated root.... repeated 4 times...

Answer 5

sorry thank you!!!

Answer 6

correct... so you were asked if 2 is a zero... its false..

Answer 7

yerp yerp yerp thank you(:

Answer 8

@joshuaknmcguire that should be "yerp yerp yerp yerp" — it's a yerp of multiplicity 4, you know :-)