Question

Factorise :- x³ – 3x² – 9x – 5

Answer 1

Let p(x) = x³ − 3x² − 9x − 5

All the factors of 5 have to be considered. These are ±1, ± 5.

By trial method,

p(−1) = (−1)³ − 3(−1)² − 9(−1) − 5

         = − 1 − 3 + 9 − 5

         = 0

Therefore, x + 1 is a factor of this polynomial.

Let us find the quotient on dividing x³ + 3x² − 9x − 5 by x + 1.

By long division,

It is known that,

Dividend = Divisor × Quotient + Remainder

∴ x³ − 3x² − 9x − 5 = (x + 1) (x² − 4x − 5) + 0

                              = (x + 1) (x² − 5x + x − 5)

                              = (x + 1) [(x (x − 5) +1 (x − 5)]

                              = (x + 1) (x − 5) (x + 1)

                              = (x − 5) (x + 1) (x + 1)