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Which of the following binomials is a factor of \(x^2 - 8x + 16\)?

A. (x - 2)
B. (x - 4)
C. (x - 8)
D. (x - 16)

User JPro
by
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2 Answers

5 votes
B. (x - 4)

that’s what fits the rules
User LongDuZboub
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2 votes

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).

User Stan Van Heumen
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