How to factorize a polynomial of degree 4?
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Factor 16x^4-81
16x4−8116x4-81
Rewrite 16x416x4 as (4x2)2(4x2)2.
(4x2)2−81(4x2)2-81
Rewrite 8181 as 9292.
(4x2)2−92(4x2)2-92
Since both terms are perfect squares, factorusing the difference of squares formula, a2−b2=(a+b)(a−b)a2-b2=(a+b)(a-b) where a=4x2a=4x2and b=9b=9.
(4x2+9)(4x2−9)(4x2+9)(4x2-9)
(4x2+9)(2x+3)(2x−3)
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