Questions: Factor. 2x^2 + x - 15

Solution Steps

The coefficients are \(a = 2\), \(b = 1\), and \(c = -15\).

The discriminant \(D\) is calculated as \(D = b^2 - 4ac = 1^2 - 4_2_-15 = 121\).

Since \(D > 0\), the quadratic expression has two distinct real roots \(x_1 = 2.5\) and \(x_2 = -3\). The factored form is \(a(x - x_1)(x - x_2) = 2(x - 2.5)(x + 3)\).

Final Answer: The factored form of the quadratic expression is 2(x - 2.5)(x + 3).