Factor the following quadratic expression:xsuperscript2end of superscript, minus− 6x minus− 16

To factor the quadratic expression x² - 6x - 16, follow these steps:

1. Identify the coefficients in the quadratic expression. In this case, a = 1 (coefficient of x²), b = -6 (coefficient of x), and c = -16 (constant term).

2. Look for two numbers that multiply to give ac (a times c, or 1*-16 = -16 in this case) and add up to b (-6 in this case). The numbers that satisfy these conditions are -8 and 2 because -8*2 = -16 and -8 + 2 = -6.

3. Rewrite the middle term of the quadratic expression as the sum of the terms -8x and 2x. This gives us x² - 8x + 2x - 16.

4. Factor by grouping. The first two terms can be grouped together, and the last two terms can be grouped together. This gives us (x² - 8x) + (2x - 16).

5. Factor out the greatest common factor from each group. From the first group, we can factor out x to get x(x - 8). From the second group, we can factor out 2 to get 2(x - 8).

6. Now, you should have two terms that look like this: x(x - 8) + 2(x - 8). Since (x - 8) is a common factor, we can factor it out to get (x - 8)(x + 2).

So, the factored form of the quadratic expression x² - 6x - 16 is (x - 8)(x + 2).