Question

use the factor theorem to factorise the following polynomial x^3-13x-12 by long division method​

Answer 1

Answer:

x³-13x-12=0

factors of 12=±1,±2,±3,±4,±6,±12

so if x=-1

(-1)³-13(-1)-12=-1+13-12=0

if x=-1 therefore (x+1) is a factor

dividing x³-13x-12 by (x+1)

from that we use our long division and I got x²-x-2 to be a factor

factorizing this we get x²-2x-x-2=0

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

so therefore we conclude that the answer to x³-13x-12=(x+1)(x-1)(x-2)