# Factorize of the Following Polynomials: X3 + 13x2 + 31x − 45 Given that X + 9 is a Factor - Mathematics

Factorize of the following polynomials:

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

#### Solution

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).

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#### APPEARS IN

RD Sharma Mathematics for Class 9
Chapter 6 Factorisation of Polynomials
Exercise 6.5 | Q 15.1 | Page 33