Thread: polynomial and factor theorem

Hi guys could you check over what i have done and point me in the right direction with part ii

i had to use polinomial division to find the remainder 3x-1 / 9x^5-4x^4

i got the remainder to be 1x or (x) is this correct?
part ii

show using factor theorem that 2x-1 is a factor of 2x^4-x^3-6x^2+5x-1
and express 2x^4-x^3-6x^2+5x-1 as a linear and cubic factor.

TBH i dont know where to start with this one

any guidance appreciated

try using long division... divide the polynomial by (2x-1), and if there is 0 remainder, that means it is a factor. Also, the division should yield a cubic function, so expressing it as a product of a linear factor and a cubic factor should look like this:

(2x-1)(the cubic function you get from division)

Right i see it now thanks for the help,

was my first part correct or was i way off?


regards

Originally Posted by tommoturbo

Show using factor theorem that is a factor of 2x^4-x^3-6x^2+5x-1

The factor theorem states that a polynomial ) has a factor if and only if = 0. So to show that is a factor of , you plug in for x in and see if it yields to zero. If it does (which it hopefully will), then by the factor theorem, is a factor of ; but if it doesn't, then is a not a factor of . Was that clear? If not, see the spoiler:

Spoiler:

First, solve :

Then substitute for in :

=

Thus, by the factor theorem, is a factor of .

Express as a linear and cubic factor.

It's asking you to express it in the form . Like this:

=

We know that is a factor , so we have:



Now, find and you are done.

Hint:

Spoiler:

Wow thanks very much that has explained it fully, the notes in my lesson where limited to two examples and i hadnt grasped it at all



thank you!