Question

How can we factorise the expression: 2x^6+17x^3+8?​

Answer 1

`(a + 2)( {a}^(2) - 2a + 4 )(2 {x}^( 3) + 1)`

Explanation:

`2x^6+17x^3+8 \\ = 2x^6+16x^3 + {x}^(3) +8 \\ = 2{x}^(3) ( {x}^(3) + 8) + 1( {x}^(3) + 8) \\ = ( {x}^(3) + 8)(2 {x}^( 3) + 1) \\ = ( {x}^(3) + {2}^(3) )(2 {x}^( 3) + 1) \\ = (a + 2)( {a}^(2) - 2a + {2}^(2) )(2 {x}^( 3) + 1) \\ = (a + 2)( {a}^(2) - 2a + 4 )(2 {x}^( 3) + 1) \\`