Factorise
\[ \begin{align}
&9x^2 - 17x - 2
\end{align} \ \]
Check the coefficient of the square of the pronumeral
The coefficient of x2 is 9. This has two pairs of factors: 3 and 3, and 9 and 1. So use the preliminary factorisation form
\[ \begin{align}
9x^2 - 17x - 2 &= \frac{(9x + m)(9x + n)}{9}
\end{align} \ \]
Find the relationships the numbers m and n satisfy?
From the preliminary factorisation method, the numbers m and n satisfy
\[ \begin{align}
mn &= -18 \\
m + n &= -17
\end{align} \ \]
Solve for m and n
The pair
\[ \begin{align}
m &= -18 \quad \text{and} \quad n = 1
\end{align} \ \]
satisfies
Substitute these in the preliminary factorisation
\[ \begin{align}
\frac{(9x - 18)(9x + 1)}{9} &= \frac{9(x - 2)(9x + 1)}{9} \\
&= (9x + 1)(x - 2)
\end{align} \ \]
So the factorisation is
\[ \begin{align}
9x^2 - 17x - 2 &= (9x + 1)(x - 2)
\end{align} \ \]
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