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