x^2+7x-30 (x+10)(x-7) (x-10)(x+3) (x+10)(x+3) (x+10)(x-5)

To factor the quadratic expression \(x^2 + 7x - 30\), we need to find two numbers that multiply to \(-30\) (the constant term) and add up to \(7\) (the coefficient of the linear term).<br /><br />Let's list the pairs of factors of \(-30\):<br /><br />- \(1\) and \(-30\)<br />- \(-1\) and \(30\)<br />- \(2\) and \(-15\)<br />- \(-2\) and \(15\)<br />- \(3\) and \(-10\)<br />- \(-3\) and \(10\)<br />- \(5\) and \(-6\)<br />- \(-5\) and \(6\)<br /><br />Among these, the pair that adds up to \(7\) is \(-3\) and \(10\).<br /><br />Thus, we can factor the quadratic as:<br /><br />\[<br />x^2 + 7x - 30 = (x - 3)(x + 10)<br />\]<br /><br />Therefore, the correct factorization is \((x - 3)(x + 10)\).