Question

Factor completely, then place the factors in the proper location on the grid. x2n 10xn 16

Options:
a) (x^n + 2)(x^n - 8) and (x^n + 4)(x^n - 4)
b) (x^n - 4)(x^n + 4) and (x^n - 2)(x^n + 8)
c) (x^n + 8)(x^n - 2) and (x^n + 4)(x^n - 4)
d) (x^n + 4)(x^n - 4) and (x^n + 2)(x^n - 8)

Answer 1

The correct factored form of the expression x2n - 10xn + 16 is (xn - 2)(xn - 8), which corresponds to option a).

Step-by-step explanation:

To factor the given expression completely, we need to find two binomial factors that will give us the original trinomial when multiplied together. The given expression is x2n - 10xn + 16. We are looking for two numbers that multiply to 16 (the constant term) and add up to -10 (the coefficient of the middle term).

The factors of 16 that add up to -10 are -2 and -8. Substituting these into two binomials that multiply to the original quadratic expression, we get:

• (xn - 2)(xn - 8)

This is the only pair of factors that meet the criteria, so the correct answer would be option a) (xn + 2)(xn - 8).