x^3-2x^2-3x+4 -- when is y axis at 0

[rigid raptor]

x^3-2x^2-3x+4

How do I factor this by the way?

I don't see any common monomial factors. Rational root theorem does not help, no special cases, and can't factor by grouping. Maybe if I could manipulate the expression somehow but I am lost on how to begin thinking in a way to factor this.

[hardy dust]

by observation you can see that x-1 is a factor of this polynomial

[hardy dust]

or you can set it equal to zero
and have to find out a solution by observation too
which will be 1 in this case

[rigid raptor]

using synthetic division I get a remainder of 10, when dividing by 1 (which is (x-1) ) . please help me see past my confusion.

[hardy dust]

but how?

I am getting 0

[rigid raptor]

maybe i am doing the division wrong

lemme take a pic

[thick kelp]

Btw, don't use any division to check for factors. Instead use the remainder theorem

[paper ore]

I can hel you

[thick kelp]

Your input is not correct. Top row should be 1 -2 -3 4

[rigid raptor]

Ah

I get confused as to when to add the negative sign

as I understand 2 - 2 is not that same as 2 - (-2)

[hardy dust]

yeah definitely it is true

[rigid raptor]

so in 2-2x the coeffiecent in the second term is -2

not +2

[hardy dust]

yes

[rigid raptor]

1 - 2(x+1) = 1 -2x -2

yes