Question

Does anybody know how to find out which of these is a facetor of the polynomial x^3-6x^2-1x+6
a)x+2
b)x-6
c)x-2
d)x+3

the correct answer is b)x-6 (but I don't know how to find it, may someone please help me)

Answer 1

factor by grouping:

x^3 - 6x^2 - 1x + 6
(x^3 - 6x^2) - 1(x - 6) (note the change of sign!)

now factor the first part:

x^2(x-6) - 1(x-6)

do you see a common factor to the two terms?

Answer 2

yes x-6

Answer 3

ohhhhhhhh

Answer 4

ok thanks

Answer 5

so you can write that as (x^2-1)(x-6)

but wait, there's more! x^2-1 is the difference of squares, so we can write it as
(x-1)(x+1)(x-6)

because (a^2-b^2) = (a-b)(a+b)