` a) ` ` 32x - 8x^{2} + 2x^{2} `
` = 2x(16 - 5x) `
` x^{3} + 64 `
` = (x + 4)(x^{2} - 4x + 16) `
` b) ` ` 9 - (x + 5)^{2} `
` = (3 - x - 5)(3 + x + 5) `
` = -(x + 2)(x + 8) `
` x^{2} + 4x + 4 `
` = (x + 2)^{2} `
` c) ` ` 5x^{3} + 5x `
` = 5x(x^{2} + 1) `
` x^4 - 1 `
` = (x^{2} - 1)(x^{2} + 1) `
` = (x - 1)(x + 1)(x^{2} + 1) `
` d) ` ` x^{2} + 5x + 6 `
` = x^{2} + 2x + 3x + 6 `
` = x(x + 2) + 3(x + 2) `
` = (x + 2)(x + 3) `
` x^{2} + 4x + 4 `
` = x^{2} + 2.x.2 + 2^2 `
` = (x + 2)^2 `