Question

factories
x^4 + 4
x^6 - 7x^3 +8

Answer 1

hey mate,

$1) {x}^{4} + 4 \\ = ( {x}^{4} + {4x}^{2} + 4) - {4x}^{2} \\ = {( {x}^{2} + 2})^{2} - {(2x)}^{2} \\ = ( {x}^{2} + 2 + 2x)( {x}^{2} + 2 - 2x) \\ = ( {x}^{2} + 2x + 2)( {x}^{2} - 2x - 2)$
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$2) {x}^{6} - {7x}^{3} + 8 \\ = { ({x}^{3}) }^{2} - 7 ({x}^{3} ) - 8 \\ = ( {x}^{3} - 8)( {x}^{3} + 1) \\ = ( {x}^{3} - {(2)}^{3} )( {x}^{3} + {(1)}^{3} ) \\ recall \: that \\ {a}^{3} + {b}^{b} = (a + b)( {a}^{2} - ab + {b}^{2} ) \\ = (x - 2)( {x}^{2} + 2x + 4)(x + 1)( {x}^{2} - x + 1)$



I hope this helps you!
@vaibhav