Question

factorise
1. 8x^4+14x^2-4
2. x^3-7x+6
3. x^6-64

Answer 1

1:
$1)8 {x}^{4} + 14 {x}^{2} - 4 \\ = > 2(4 {x}^{4} + 8 {x}^{2} - {x}^{2} - 2) \\ = > 2(4 {x}^{2} ( {x}^{2} + 2) - ( {x}^{2} + 2)) \\ = > 2( {x}^{2} + 2)(4 {x}^{2} - 1) \\ = > ( {x}^{2} + 2)(2x - 1)(2x + 1) \\ \\ 2) {x}^{3} - 7x + 6 \\ = > {x}^{3} - {x}^{2} + {x}^{2} - 7x + 6 \\ = > {x}^{2} (x - 1) + (x - 6)(x - 1) \\ = > (x - 1)( {x}^{2} + x - 6) \\ = > (x - 1)(x - 2)(x + 3) \\ \\ 3) {x}^{6} - 64 \\ = > ( {x}^{3} + 8)( {x}^{3} - 8) \\ = > (x + 2)( {x}^{2} - 2x + 4)(x - 2) \\ ({x}^{2} + 2x + 4)$