Question

Factorise x⁴+x²+1 using formula​

Answer 1

Question: Factorise x⁴+x²+1 using formula​

One way to get answer: 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]

Another way: x⁴+x²+1

=x⁴+2x²-x²+1

=(x⁴+2x²+1)-x²

=[(x²)²+2x²+(1)²]-x²

=(x²+1)²-x²

=(x²+1+x)(x²+1-x). Ans.