27 Write the polynomial fx x3x 6 in its factored form given

27. Write the polynomial f(x) = x3-x 6 in its factored form given that (x-2) is a factor.

Solution

Since we know (x-2) is a factor of x³ -x-6

Hence we divide f (x) by (x-2) to get it factorised.

(X-2) | x³ -x -6 | x² +2x+3

-x³+2x²

^__________

  2x²-x

-2x²+4x

_________________

3x-6

-3x+6

_________

0

Thus (x-2)(x²+2x+3)= x³-x-6