Factorize each of the following expressions : (i) `4sqrt(3)x^2+5x-2sqrt(3)`, (ii) `5sqrt(5)x^2+30 x+8sqrt(5)`,

Explanation

(i)`4sqrt(3) x^2 +5x -2sqrt(3) =0`
`⇒4sqrt(3) x^2 +8x -3x -2sqrt(3)=0`
`⇒4x(sqrt(3) x+2) -sqrt(3)(sqrt(3)x +2) =0`
`⇒(sqrt(3)x +2)(4x -sqrt(3)) =0`
`⇒(sqrt(3)x +2) =0` or `(4x-sqrt(3)) =0`
`⇒x = -2/sqrt(3)` or `sqrt(3)/4`
(ii) `5sqrt(5)x^2+30 x+8sqrt(5)`
`5sqrt(5)x² + 30x + 8sqrt(5)`
Splitting the middle term
`= 5sqrt(5)x^2 + 20x + 10x + 8sqrt(5)`
`= 5sqrt(5)x^2 + 4 xx 5x + (2sqrt(5) ) xx sqrt(5) x + 2sqrt(5) xx 4`
`= 5x (sqrt(5)x + 4 ) + ( 2sqrt(5) ) [ sqrt(5)x + 4 ]`
`= ( sqrt(5)x + 4 ) ( 5x + 2sqrt(5) )`