Question

f(x) = x3 + 3x2 - x - 3

Part A: What are the factors of f(x)? Show your work. How do I factor this when the 3 doesn't have any factors and the x has no coefficient?

Answer 1

f(x) = x2(x+3) - 1(x+3)

Answer 2

f(x) = (x2 -1) (x+3)

Answer 3

to do these first you want to regroup the 1st and 2nd term
then regroup the 3rd and fourth term

Answer 4

I knew that, forgot about the invisible one next to x thnks :)

Answer 5

then factor out the x^2 and -1
then you can rewrite it as (x^2 -1)(x+3)

Answer 6

you're welcomed :)

Answer 7

Could you help me out with the second and third part?

Answer 8

sure, the second step that I do this problem?

Answer 9

or another question?

Answer 10

Part B: What are the zeros of f(x)? Show your work. but the zeros are just -1 and 3 for this?

Answer 11

set x2-1 = 0
now find x
set x+3 = 0
find x

so to do these, set factors of the equation equate to 0.

Answer 12

nope, x2 = 1
when you square root 1 , you get -1 AND 1

Answer 13

1 squared = 1
-1 squared = 1

Answer 14

Oh so 1 and -3 x^2 -1 =0 ---> x^2 = 1 and same with second

Answer 15

so (1,0) and (-3, 0)

Answer 16

(-1,0) (1,0) (3,0)

Answer 17

*** (-3,0) I mean not (3,0)

Answer 18

\[x^{2} = 1\]
x= 1, -1


because
\[(-1) ^{2} = 1 \]
and
\[1^{2} = 1\]

Answer 19

Could you explain how you got 3? I'm still confused on that part.

Answer 20

I said (-3,0) not (3,0) :)
it was a typo from before

CONCLUSION
(-1,0)(1,0) (-3,0)

Answer 21

ok

Answer 22

art C: What are the steps you would follow to graph f(x)? Describe the end behavior of the graph of f(x). I think i got this down except I don't know if graph going left or right

Answer 23

use the 0s to graph it, then end behavior starts from down to up

Answer 24

just plot the 0s first

Answer 25

Ok I think I'm good now thanks for all help.

Answer 26

glad it helps :)