Question

What is the factor of x^3-4x^2+x+6?

Answer 1

here is a good gimmick to know:
it is going to be easy to factor if you can find the zeros
math teachers usually make a zero of 1 or -1 because those are the easiest, so check those first

Answer 2

1 does not work, because if you plug it in to \(x^3-4x^2+x+6\) you get
\[1-4+1+6\] which is not zero

Answer 3

but \(-1\) does work, you get
\[-1-4-1+6=0\]

Answer 4

therefore you know it factors
\[x^3-4x^2+x+6=(x+1)(something)\] and you can find the "something" either by division (synthetic division is easiest) or by thinking

Answer 5

your choice

Answer 6

What divisor can i use in synthetic division?

Answer 7

you want to factor \(x^3-4x^2+x+6\) as \((x+1)(whatever)\) this makes
\[whatever=(x^3-4x^2+x+6)\div (x+1)\]

Answer 8

you can also just figure out what it has to be in your head more or less

Answer 9

i got 3x

Answer 10

how?
\[x^3-4x^2+x+6=3x(x-1)?\] that can't be correct, can it?

Answer 11

No, it's wrong. :3

Answer 12

actually i meant to write
\[x^3-4x^2+x+6=3x(x+1)?\] but that is not correct either
your "whatever" needs to be a polynomial of degree 2

Answer 13

it is clear what you have to do? you have to write
\[x^3-4x^2+x+6=(x+1)(ax^2+bx+c)\]