Đáp án:
$ 1. $
` a) ` ` x^4 + 4 `
` = x^4 + 4 + 4x^2 - 4x^2 `
` = (x^4 + 4x^2 + 4) - 4x^2 `
` = (x^2 + 2)^2 - (2x)^2 `
` = (x^2 + 2 - 2x)(x^2 + 2 + 2x) `
` b) ` ` x^4 + x^2 + 1 `
` = x^4 - x^3 + x^3 + x^2 - x^2 + x^2 + x - x + 1 `
` = (x^4 - x^3 + x^2) + (x^3 - x^2 + x) + (x^2 - x + 1) `
` = x^2 (x^2 - x + 1) + x(x^2 - x + 1) + (x^2 - x + 1) `
` = (x^2 - x + 1)(x^2 + x + 1) `
$ 2. $
` x^3 + 4x^2 - 3x - 18 `
` = x^3 - 2x^2 + 6x^2 - 12x + 9x - 18 `
` = x^2 (x - 2) + 6x(x - 2) + 9(x- 2) `
` = (x - 2)(x^2 + 6x + 9) `
` = (x - 2)(x + 3)^2 `
Vì ` (x + 3)^2 ≥ 0 ` $∀x$
Mà ` x ≥ 2 → x - 2 ≥ 0 `
`⇒ ( x - 2 ) ( x + 3 ) 2 ≥ 0 ( đ.p.c.m )`
