Final answer:
The binomial factor of the quadratic equation x^2 - 8x + 16 is (x - 4), which is option B.
Step-by-step explanation:
The student has asked which of the following binomials is a factor of x2 - 8x + 16. To determine the factor, we look for a binomial that when multiplied by itself will give us the original quadratic equation.
We are effectively looking to factor the quadratic expression. If we notice the pattern, this is a perfect square because (4)2 = 16 and 2(4)(x) = 8x. Therefore, the binomial that will satisfy this condition is (x - 4).
Considering that the quadratic is in the form of ax2 + bx + c, and we see that a = 1, b = -8, and c = 16, we can also use the square root method or complete the square to find that (x - 4)2 = x2 - 8x + 16. Hence, the factor of the quadratic is (x - 4).