Question

PLEASE HELP!!!!!!

A function is shown below:

f(x) = x3 + 5x2 - x - 5

Part A: What are the factors of f(x)? Show your work.

Answer 1

since \(f(1)=0\) this will factor as \((x-1)(something)\)

Answer 2

ok, and?

Answer 3

@satellite73 ?

Answer 4

you have a couple of choices
you can do long division (a pain )
you can use synthetic division (easiest)
or you can think (requires thinking)

Answer 5

i cannot write the first two methods here it is annoying
we can use the think method if you like

Answer 6

ok :)

Answer 7

lol

Answer 8

\[x^3 + 5x^2 - x - 5=(x-1)(ax^2+bx+c)\] and \(a\) and \(c\) are pretty obvious right?

Answer 9

no

Answer 10

what are a and c?

Answer 11

ok lets go slow
first we know that \(x-1\) is a factor because \(f(1)=0\) right?

Answer 12

right

Answer 13

that means
\[x^3+5x^2-x-5=(x-1)(something)\]

Answer 14

and the "something" has to be a quadratic (degree two) because when you multiply out you have to get a polynomial of degree three, namely \(x^3+5x^2-x-5\)

Answer 15

right

Answer 16

so what can that quadratic be?

Answer 17

um, x^2 + 5x - 5?

Answer 18

well i don't know
maybe

Answer 19

\[x^3 + 5x^2 - x - 5=(x-1)(ax^2+bx+c)\] is what i wrote and i said that \(a\) is obvious because it is \(a=1\) for sure because when you multiply out you have to get \(x^3\)

Answer 20

and \(c=5\) not \(-5\) because when you multiply out you need to end up with \(-5\)

Answer 21

right. so the factors are (x-1) (x + 1) and (x + 5) ?

Answer 22

yes

Answer 23

ok thanks :)

Answer 24

yw