Factor. 9z^2-18z-7 square square

To factor the quadratic expression $9z^2 - 18z - 7$, we need to find two numbers that multiply to give the product of the coefficient of $z^2$ term (9) and the constant term (-7), which is -63, and add up to the coefficient of the $z$ term, which is -18.<br /><br />The two numbers that satisfy these conditions are -21 and 3, since:<br />-21 * 3 = -63<br />-21 + 3 = -18<br /><br />Now, we can rewrite the middle term (-18z) using these two numbers:<br />$9z^2 - 21z + 3z - 7$<br /><br />Next, we group the terms:<br />$(9z^2 - 21z) + (3z - 7)$<br /><br />Factor out the greatest common factor from each group:<br />$3z(3z - 7) + 1(3z - 7)$<br /><br />Now, we can factor out the common binomial factor $(3z - 7)$:<br />$(3z - 7)(3z + 1)$<br /><br />Therefore, the factored form of $9z^2 - 18z - 7$ is:<br />$(3z - 7)(3z + 1)$