Question

What is the completely factored form of d4 - 8d2 + 16?. A) (d2 + 4)(d2 - 4). B) (d2 - 4)(d2 - 4). C) (d2 + 4)(d + 2)(d - 2). D) (d + 2)(d - 2)(d + 2)(d - 2)

Answer 1

For a quadratic equation, the negative of the numerical coefficient of the second term is the sum of the roots and the constant is their product. Let a and b be the roots such that,
                                      a + b = 8
                                        ab = 16
The values of a and b are 4 and 4. Such that the factors are,
                                        (d² - 4)(d² -4)
Both the factors are difference of two squares. The final answer for this item is,
                                  (d + 2)(d - 2)(d + 2)(d - 2)

This is letter D.