Question

A function is shown below:
f(x) = x^3 + 5x^2 - x - 5
Part A: What are the factors of f(x)? Show your work.
Part B: What are the zeros of f(x)? Show your work.
Part C: What are the steps you would follow to graph f(x)? Describe the end behavior of the graph of f(x).

Answer 1

@UnkleRhaukus may you please help me? I really need to get this done and id love for you to help!

Answer 2

\[f(x)=x^3 + 5x^2 - x - 5\]

look at the first two terms
\[x^3 \text{ and } 5x^2\]
what is a common factors of these?

Answer 3

are you there ? @Floridagirl10

Answer 4

yes sorry this website is slow for me... in order to find the common factor of those two.. wouldn't x^@ be 1x^2 ? the common factor would be 1...? @UnkleRhaukus

Answer 5

yeah openstudy is having some issues at the moment,

i'm not quite sure what you'r saying,
are you saying the common of x^3 and 5x^2 is x^2 ?

Answer 6

I honestly don't know im lost right now.. Sorry. Well I think I am saying that the common factor is x^2. when im typing it doesn't come up til after I send it so I ciouldnt see it.

Answer 7

ok well in that case you are correct! the common factor is x^2

This means we can write \[x^3+5x^2\]as\[x^2(\,\cdots\,+\,\cdots\,)\]

[fill in the blanks]

Answer 8

would it be x^2(x+5) ? @UnkleRhaukus

Answer 9

Excellent!
so we have factored the equation a little

\[f(x)= x^3 + 5x^2 - x - 5\\
\qquad=x^2(x+5)-x-5\]

Answer 10

Now lets look at the last two terms -x and -5

what is the common factor this time?

Answer 11

Im not sure about this one.. :/

Answer 12

they are both negative right?

Answer 13

you could write -x as (-1)(x)
and -5 as (-1)(5)

Answer 14

so the common factor here is -1

This means we can write
-x -1
as
-( ⋯ + ⋯ )

what are the blanks?

Answer 15

iit will be -(x+1)? or is it -1?

Answer 16

whoops i mean

-x -5
becomes
-( ⋯ + ⋯ )