The factored form of the polynomial f(x) is: (x + 8)(x - 2)
Here's how to factor the polynomial f(x):
1. Identify the coefficient of the leading term, the coefficient of the middle term, and the constant term:
Leading term coefficient (x^2): 1
Middle term coefficient (x): 6
Constant term: -16
2. Find two values that add up to the middle term coefficient (6) and multiply to the constant term (-16).
In this case, the values 8 and -2 satisfy these conditions:
8 + (-2) = 6
8 * (-2) = -16
3. Rewrite the polynomial with these values replacing the middle term coefficient:
f(x) = x^2 + 8x - 2x - 16
4. Group the terms and factor by grouping:
Group the first two terms and the last two terms:
f(x) = (x^2 + 8x) + (-2x - 16)
Factor out common factors:
f(x) = x(x + 8) - 2(x + 8)
5. Factor out the remaining common factor (x + 8):
f(x) = (x + 8)(x - 2)
Therefore, the factored form of the polynomial f(x) is: (x + 8)(x - 2)