Question

Factorise x^3 + 2x^2 - 5x – 6 by using factor theorem.​

Answer 1

Answer:

x³+2x²-5x-6=0

factors of 6=±1,±2,±3,±6

so therefore inserting our x to be -1 we get

(-1)³+2(-1²)-5(-1)-6=-1+2+5-6; which is equal to 0

therefore (x+1) is a factor

inserting x to be 2

(2)³+2(2²)-5(2)-6=8+8-10-6=0

therefore (x-2) is a factor

inserting x to be -3

(-3)³+2(-3²)-5(-3)-6=-27+18+15-6=0

therefore (x+3) is a factor

we can then conclude that x³+2x²-5x-6=(x+1)(x-2)(x+3)

I hope this helps