resolve into factors : (i)x⁴+x²+1
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x⁴+ x² + 1
x⁴+ 1 + x²
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)
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x⁴+ 1 + x²
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)
If you like it follow me and punch the brainiest button.
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