factorise x^4+x^2+1
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Consider x4 + x2 + 1 = (x4 + 2x2 + 1) – x2 = [(x2)2 + 2x2 + 1] – x2 = [x2 + 1]2 – x2 It is in the form of (a2 – b2) = (a + b)(a – b) Hence [x2 + 1]2 – x2 = [x2 + 1 + x] [x2 + 1 – x]
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Consider x4 + x2 + 1
= (x4 + 2x2 + 1) – x2
= [(x2)2 + 2x2 + 1] – x2
= [x2 + 1]2 – x2
It is in the form of (a2 – b2) = (a + b)(a – b)
Hence [x2 + 1]2 – x2 = [x2 + 1 + x] [x2 + 1 – x]
Step-by-step explanation:
so we need to add and substract x2
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