Question

Which statement about the function below is true?

f(x) = x^3 5x^2 25x + 125 = (x + 5)(x 5)(x 5)

(Points : 4)
The root 5 has a multiplicity of 1.

The root 5 has a multiplicity of 2.

The root 5 has a multiplicity of 1.

The root 5 has a multiplicity of 3.

Answer 1

@undeadknight26 @InfiniteMinds

Answer 2

the first 2 are minus and so are the last two

Answer 3

im confused o-o

Answer 4

@andrewhaze

Answer 5

So you are saying:

\(f(x) = x^3-5x^2-25x + 125 = (x + 5)(x-5)(x-5)\)

And basically what they want to know is when would x=5.

Answer 6

yes

Answer 7

ill let @e.mccormick help xP

Answer 8

OK. So, for any \((x\pm a)\) factor you flip the sign to say \(x=\mp a\)

So the factor (x+1) means x = -1.

Now, if you apply that, how many are equal to 5?

Answer 9

2

Answer 10

Yep.

Answer 11

so B

Answer 12

And there you go.

Graphically you can see it just touches, not crosses, at that point:
https://www.desmos.com/calculator/g9tddezcnm

Answer 13

Thank youuu!!!