Question

Find the value of k so that the polynomial
3 − 3² − 4 + k is divisible by (x+2). Hence factorise
the polynomial.

Answer 1

It looks the polynomial is x^3-3x^2-4x+k. For finding value of k subs x= -2 and eqt to 0. We get k=12. substituting in the above equation and dividing by (x+2) we get (x^2- 5x+6) . The roots of latter are 2 and 3. Hence all three roots of polynml are - 2,2 and 3.