Factor \( x^{2}+x-20 \)

To factor the quadratic expression \( x^2 + x - 20 \), we need to look for two numbers that multiply to \(-20\) (the constant term) and add up to \(1\) (the coefficient of \(x\)). The numbers \(5\) and \(-4\) fit the bill since \(5 \times -4 = -20\) and \(5 + (-4) = 1\). Therefore, we can express the factored form as: \[ (x + 5)(x - 4) \] This shows how the roots of the equation are derived from the factors. When you set each factor equal to zero, \(x + 5 = 0\) leads to \(x = -5\) and \(x - 4 = 0\) leads to \(x = 4\). When we apply factoring in the real world, we often encounter it in areas like physics or engineering where we need to simplify equations for better computation. For example, when determining the trajectory of an object, such as a projectile, you might find a quadratic that needs simplifying to understand its maximum height or distance travelled.