We the Bark 10 points x^2-3x-70 like (x+a)(x+b) a=type your answer. b. tope your answer...

To factor the quadratic expression \(x^2 - 3x - 70\) in the form \((x + a)(x + b)\), we need to find two numbers \(a\) and \(b\) such that:<br /><br />1. Their product is equal to the constant term, which is \(-70\).<br />2. Their sum is equal to the coefficient of the linear term, which is \(-3\).<br /><br />Let's find the factors of \(-70\) and see which pair adds up to \(-3\):<br /><br />\[<br />\begin{array}{|c|c|}<br />\hline<br />\text{Factors of } -70 & \text{Sum of factors} \\<br />\hline<br />-1 \cdot 70 & -1 + 70 = 69 \\<br />1 \cdot -70 & 1 - 70 = -69 \\<br />-2 \cdot 35 & -2 + 35 = 33 \\<br />2 \cdot -35 & 2 - 35 = -33 \\<br />-5 \cdot 14 & -5 + 14 = 9 \\<br />5 \cdot -14 & 5 - 14 = -9 \\<br />-7 \cdot 10 & -7 + 10 = 3 \\<br />7 \cdot -10 & 7 - 10 = -3 \\<br />\hline<br />\end{array}<br />\]<br /><br />From the table, we can see that the pair \(-7\) and \(10\) adds up to \(-3\). Therefore, the correct values for \(a\) and \(b\) are:<br /><br />\[<br />a = -7, \quad b = 10<br />\]<br /><br />So, the factored form of the quadratic expression \(x^2 - 3x - 70\) is:<br /><br />\[<br />(x - 7)(x + 10)<br />\]