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How do I factor x^8-80x^4-81

User Prasad D
by
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1 Answer

5 votes

Which two numbers add up to -80 and multiply to -81?

-81 and 1

Rewrite the expression using the above

(x^4 - 81)(x^4 + 1)

Rewrite x^4 - 81 in the form; a^2 - b^2, where a = x^2 and b = 9

((x^2)^2 - 9^2)(x^4 + 1)

Use the Difference of Squares: a^2 - b^2 = (a + b)(a - b)

(x^2 + 9)(x^2 - 9)(x^4 + 1)

Rewrite x^2 - 9 in the form a^2 - b^2, where a = x and b = 3

(x^2 + 9)(x^2 - 3^2)(x^4 + 1)

Use the Difference of Squares; a^2 - b^2 = (a + b)(a - b)

(x^2 + 9(x + 3)(x - 3)(x^4 + 1)

User Jasim Khan Afridi
by
5.5k points
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