Giải thích các bước giải:
Bài 1:
f(x) = x² + 6x - 16
Cách 1 :
x² + 6x - 16 = x² + 8x - 2x - 16
= (x² + 8x) - (2x + 16)
= x(x + 8) - 2(x + 8)
= (x - 2)(x + 8)
Cách 2 :
x² + 6x - 16 = x² + 6x + 9 - 25
= (x² + 6x + 9) - 25 = (x + 3)² - 5²
= (x + 3 - 5)(x + 3 + 5) = (x -2)(x +8)
Cách 3 :
x² + 6x - 16 = x² - 4 + 6x - 12
= (x² - 4) + (6x - 12)
= (x -2)(x +2) + 6(x - 2)
= (x - 2)(x + 2 + 6 ) = (x - 2)(x + 8)
Cách 4 :
x² + 6x - 16 = x² + 6x + 48 - 64
= (x² - 64) + (6x + 48)
= (x - 8)(x + 8) + 6(x + 8)
= (x + 8)(x - 8 + 6) = (x + 8)(x - 2)
Cách 5 :
x² + 6x - 16
= 2x² - x² + 6x - 128 + 112
= (2x² - 128) - (x² - 6x - 112)
= 2(x² - 64) - (x² - 14x + 8x - 112)
= 2(x - 8)(x + 8) - [(x² - 14x) + (8x - 112)]
= (2x - 16)(x + 8) - [ x(x - 14) + 8(x - 14)]
= (2x - 16)(x + 8) - (x + 8)(x - 14)
= (x + 8)(2x - 16 - x + 14)
= (x + 8)(x - 2)
Bài 2 :
f(x) = 3x² - 5x - 22
Cách 1 :
3x² - 5x - 22 = 3x² - 11x + 6x - 22
= (3x² - 11x) + (6x - 22)
= x(3x - 11) + 2(3x - 11)
= (3x - 11)(x + 2)
Cách 2 :
3x² - 5x - 22
= 3x² - 12 - 5x - 10
= (3x² - 12) - (5x + 10)
= 3(x² - 4) - 5(x + 2)
= 3(x - 2)(x + 2) - 5(x + 2)
= (3x - 6)(x + 2) - 5(x + 2)
= (x + 2)(3x - 6 - 5) = (x + 2)(3x -11)
Cách 3 :
3x² - 5x - 22
= 9x² - 6x² - 5x - 121 + 99
= (9x² - 121) - (6x² + 5x - 99)
= (3x - 11)(3x +11) - (6x² + 27x - 22x - 99)
= (3x - 11)(3x +11) - [(6x² + 27x) - (22x + 99)]
= (3x - 11)(3x + 11) - [ 3x(2x + 9) - 11 - (2x + 9)]
= (3x - 11)(3x +11) - (2x + 9)(3x - 11)
= (3x - 11)(3x + 11 - 2x - 9)
= (3x - 11)(x + 2)