How do you solve #2x^3-6x^2+x-1<=2x-3?#

1 Answer
Alicia
May 9, 2017

Firstly set it #=# to #0# by taking away #2x-3# from both sides.
This leaves us with:
#2x^3 - 6x^2 - x +2 <= 0#
Then we can use the factor theorem to find one of our roots.
Start with #f(x) = 1#
#2(1)^3 -6(1)^2 -(1) +2 = -3# Not a factor
Try #2#
#2(2)^3 -6(2)^2 -(2) +2 = -8# Not a factor
Try #-1#
#2(-1)^3 -6(-1)^2 -(-1) +2 = -7# Not a factor
Try #-2#
#2(-2)^3 -6(-2)^2 -(-2) +2 = -36# Not a factor
Try #3#
#2(3)^3 -6(3)^2 -(3) +2 = -1# Not a factor
Try #4#
#2(4)^3 -6(4)^2 -(4) +2 = 30# Not a factor.

Very sorry I think I've done something wrong but I thought I'd send you my working a)because I find sometimes reading what someone else has done, even if wrong, helps to solve things and b)because I cant bring myself to get rid of that working.

It could be possible that you just need a factor higher than I'm using so feel free to try some, and if so you'll need to do some algebraic long division. Happy to show you this if you find a factor!

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