Question

Show that x-2 is a factor of x³+2x²-5x-6

Answer 1

Let f (x) = x^3 + 2x^2 - 5x - 6
From factor theorem...
we know that.if (x-2) us a factor of f (x)
then f (2) should be equal to 0.
So check the value of f (2) ,,,
f (2) = 2^3 + 2 (2)^2 - 5 (2) - 6
= 8 + 8 -10 -6
= 16 - 16 = 0
here, f (2) = 0
Hence this show that (x-2) is a factor of f (x).