Factorize : `x^3+13 x^2+31 x-45` given that `x+9` is a factor

Explanation

To factorize the polynomial \( x^3 + 13x^2 + 31x - 45 \) given that \( x + 9 \) is a factor, we will use polynomial long division.

### Step 1: Set up the long division
We will divide \( x^3 + 13x^2 + 31x - 45 \) by \( x + 9 \).

### Step 2: Divide the leading terms
Divide the leading term of the dividend \( x^3 \) by the leading term of the divisor \( x \):
\[
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