Questions: Factor the given trinomial. If the trinomial cannot be factored, indicate "Not Factorable". x^2+3x-28

Solution Steps

We start with the trinomial given by

\[ x^{2} + 3x - 28. \]

To factor the trinomial, we need to find two numbers that multiply to the constant term \(-28\) and add up to the coefficient of the linear term \(3\). The numbers that satisfy these conditions are \(-4\) and \(7\) because:

\[ -4 \times 7 = -28 \quad \text{and} \quad -4 + 7 = 3. \]

Using the numbers found, we can express the trinomial as the product of two binomials:

\[ x^{2} + 3x - 28 = (x - 4)(x + 7). \]

Final Answer