`d)`
`(x^2 + 4x+8) + 3x (x^2 + 4x+8) + 2x^2`
` = [ (x^2+4x+8) + 3x(x^2+4x+8) + 9/4x^2] - 1/4 x^2`
` = [ (x^2+4x+8) + 2 . 3/2x . (x^2+4x+8) + (3/2 x)^2 ]- (1/2 x)^2`
` = (x^2 + 4x+8 + 3/2x)^2 - (1/2 x)^2`
`= (x^2+4x+8+3/2x-1/2x) (x^2+4x+8+3/2x + 1/2x)`
` = (x^2 + 5x + 8)(x^2 + 6x+8)`
` = (x^2+5x+8)(x^2 + 2x + 4x+8)`
` = (x^2+5x+8)[x (x+2) + 4(x+2)]`
`= (x^2+5x+8)(x+2)(x+4)`
`e)`
`x^4 + 6x^3 + 7x^2 -6x + 1`
` = x^4 + 9x^2 + 1 + 6x^3 - 2x^2 - 6x`
` = (x^2)^2 + (3x)^2 + 1^2 + 2 . x^2 . 3x - 2 . x^2 . 1 - 2 . 3x . 1`
` = (x^2 + 3x - 1)^2`
`f)`
`(x^2-1)^2 - 18(x+1)(x-1)`
`= (x^2 - 1)^2 - 18 (x^2 - 1)`
`= (x^2-1) (x^2 - 1-18)`
`= (x^2 -1)(x^2-19)`
`= (x-1)(x+1)(x^2-19)`
