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### Factor x^4 + 11x^2 - 80

x^4 + 11x^2 - 80 is a trinomial and can be factored by the method of splitting the middle term.

Find two number whose product is -80 and whose sum is 11. That is,

|__| * |__| = -80
|__| + |__| = 11

The two numbers are 16 and -5 because 16 times -5 is -80 and 16 - 5 is 11. Now rewrite the expression and replace 11x^2 with 16^2 - 5x^2 to get

x^4 + 16x^2 - 5x^2 - 80

Factor the expression further by grouping the four terms into two groups. The first group contains the first to terms and the second group contains the next two terms,

(x^4 + 16x^2) - (5x^2 - 80)

Factor out x^2 from the first group and -5 from the second group,

x^2(x^2 + 16) - 5(x^2 + 16)

Factor out x^2 + 16 from the expression,

(x^2 + 16)(x^2 - 5)

Thus the expression x^4 + 11x^2 - 80 is completely factored (x^2 + 16)(x^2 - 5)