x^4+x^2+1 how will it be factorized
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Hi!
x4 + x2 + 1
= x4+ x2 + 1 + x2 – x2 [Adding and subtracting x2 ]
= x4+ 2x2 + 1 – x2
= (x2 + 1)2 – x2 [ a2 + b2 + 2ab = (a + b)2 ]
= (x2 + 1 – x) (x2 + 1 + x) [ a2 – b2 = (a + b) (a – b) ]
= (x2 + x + 1) (x2 – x + 1)
Thus, x4 + x2 + 1 = (x2 + x + 1) (x2 – x + 1)
Cheers!
x4 + x2 + 1
= x4+ x2 + 1 + x2 – x2 [Adding and subtracting x2 ]
= x4+ 2x2 + 1 – x2
= (x2 + 1)2 – x2 [ a2 + b2 + 2ab = (a + b)2 ]
= (x2 + 1 – x) (x2 + 1 + x) [ a2 – b2 = (a + b) (a – b) ]
= (x2 + x + 1) (x2 – x + 1)
Thus, x4 + x2 + 1 = (x2 + x + 1) (x2 – x + 1)
Cheers!
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