Factor completely. \( 5 x^{2}-80 x-85 \) Submit

To factor the expression \(5x^2 - 80x - 85\) completely, we can start by factoring out the greatest common factor, which is 5: \[ 5(x^2 - 16x - 17) \] Next, we need to factor the quadratic \(x^2 - 16x - 17\). We can use the quadratic formula \(x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\) where \(a = 1\), \(b = -16\), and \(c = -17\): 1. Calculate the discriminant: \[ (-16)^2 - 4(1)(-17) = 256 + 68 = 324 \] 2. The square root of 324 is 18. So we have: \[ x = \frac{16 \pm 18}{2} \] This gives us two solutions: 1. \(x = \frac{34}{2} = 17\) 2. \(x = \frac{-2}{2} = -1\) Now we can express this factorization: \[ x^2 - 16x - 17 = (x - 17)(x + 1) \] Putting it all together, we have the completely factored form: \[ 5(x - 17)(x + 1) \]