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Factor x^3-12x+16. Show all work.

1 Answer

6 votes

Answer:
(x-2)^(2)(x+4)

Explanation:

For
x^(3) - 12x + 16 we can test out different values of x until the polynomial is zero, in this case 2 works so we can use long division or seperation of terms and factoring. But to show work, I will use seperation and factor.


x^(3) - 12x + 16 = x^(3) - 8 - 12x + 24 =
(x-2)(x^(2)+2x+4) -12 (x-2)

=
(x-2)(x^(2)+2x-8)

Then we can factor the second-degree polynomial to get
(x-2)(x+4)(x-2) or
(x-2)^(2)(x+4)

User Ccalboni
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