#### Question

Factorize of the following polynomials:

x^{3} + 13x^{2} + 31x − 45 given that x + 9 is a factor

#### Solution

Let f(x) = x^{3} + 13x^{2} + 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*).

Is there an error in this question or solution?

Solution Factorize of the Following Polynomials: X3 + 13x2 + 31x − 45 Given that X + 9 is a Factor Concept: Factorisation of Polynomials.