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factorise x4+x2+1 |
| Add and subtract 2(x²)(1) to make a perfect square = (x²)² ? 2(x²)(1) + 2(x²)(1) + (1)² + x² = (x² + 1)² ? 2x² + x² = (x² + 1)² ? x² = (x² + 1)² ? (x)² Factorize as difference of 2 squares, a² ? b² = (a + b)(a ? b) = [ (x² + 1) + (x) ][ (x² + 1) ? (x) ] = (x² + 1 + x)(x² + 1 ? x) = (x² + x + 1)(x² ? x + 1) |
