9х2-7х-2

To factor the quadratic expression \(9x^2 - 7x - 2\), we need to find two numbers that multiply to \(9 \times -2 = -18\) (the product of the coefficient of \(x^2\) and the constant term) and add to \(-7\) (the coefficient of \(x\)).

The numbers \(-9\) and \(2\) fit these criteria, since:

• \(-9 \times 2 = -18\)
• \(-9 + 2 = -7\)

Now we can rewrite the original expression:

\[ 9x^2 - 9x + 2x - 2 \]

Next, we can factor by grouping:

\[ = (9x^2 - 9x) + (2x - 2) \]

Factoring out the common terms from each group, we get:

\[ = 9x(x - 1) + 2(x - 1) \]

Now, we can factor out the common binomial factor:

\[ = (9x + 2)(x - 1) \]

Thus, the factored form of the quadratic expression \(9x^2 - 7x - 2\) is:

\[ (9x + 2)(x - 1) \]