Factor.x, squared, minus, 5, x, minus, 14x 2 −5x−14

The given expression is x^2 - 5x - 14. Here are the steps to factorize it:

Step 1: Identify the coefficients of the quadratic equation. Here, a = 1 (coefficient of x^2), b = -5 (coefficient of x), and c = -14.

Step 2: Find two numbers that multiply to give ac (a times c), and add to give b. In this case, ac = (1)(-14) = -14 and b = -5. The numbers that satisfy this are -7 and 2 because (-7)(2) = -14 and -7 + 2 = -5.

Step 3: Rewrite the middle term (bx) as the sum of the terms with the two numbers found in step 2. This gives us: x^2 - 7x + 2x - 14.

Step 4: Factor by grouping. The first two terms can be grouped together, and the last two terms can be grouped together. This gives us: x(x - 7) + 2(x - 7).

Step 5: Notice that (x - 7) is a common factor. Factor out (x - 7) to get: (x - 7)(x + 2).

So, x^2 - 5x - 14 factors to (x - 7)(x + 2).