Question

Factorize of the following polynomials:

x³ + 13x² + 31x − 45 given that x + 9 is a factor

Answer 1

 Let  f(x) = x³ + 13x² + 31x − 45 be the given polynomial.

Therefore (x +9) is a factor of the polynomial f(x).

Now,

`f(x) = x^2(x + 9) + 4x (4x (x+9) -5) (x+ 9)`

`= (x+9){x^2 + 4x - 5}`

` = (x+9){x^2 + 5x - x - 5}`

`= (x+9)(x-1)(x+5)`

Hence  ( x - 1),(x + 5) and (x + 9)are the factors of polynomial f(x).