Question

Bài 3: Phân tích đa thức thành nhân tử

a) x³+4x²-29x+24

b) x³+6x²+11x+6

c) 3x³-7x²+17x-5

d) 2x³-5x²+8x-3

e) 3x³-14x²+4x+3

f) x³+5x²+8x+4

Answer 1

a) x³ + 4x² - 29x + 24

= x³ + 8x² - 4x² - 32x + 3x + 24

= (x³ + 8x²) - (4x² + 32x) + (3x + 24)

= x²(x + 8) - 4x(x + 8) + 3(x + 8)

= (x + 8)(x² - 4x + 3)

= (x + 8)(x² - 3x - x + 3)

= (x + 8)[(x² - 3x) - (x - 3)]

= (x + 8)[x(x - 3) - (x - 3)]

= (x + 8)(x - 3)(x - 1)

b) x³ + 6x² + 11x + 6

= x³ + x² + 5x² + 5x + 6x + 6

= (x³ + x²) + (5x² + 5x) + (6x + 6)

= x²(x + 1) + 5x(x + 1) + 6(x + 1)

= (x + 1)(x² + 5x + 6)

= (x + 1)(x² + 2x + 3x + 6)

= (x + 1)[(x² + 2x) + (3x + 6)]

= (x + 1)[x(x + 2) + 3(x + 2)]

= (x + 1)(x + 2)(x + 3)

c) 3x³ - 7x² + 17x - 5

= 3x³ - x² - 6x² + 2x + 15x - 5

= (3x³ - x²) - (6x² - 2x) + (15x - 5)

= x²(3x - 1) - 2x(3x - 1) + 5(3x - 1)

= (3x - 1)(x² - 2x + 5)

Answer 2

d) 2x³ - 5x² + 8x - 3

= 2x³ - x² - 4x² + 2x + 6x - 3

= (2x³ - x²) - (4x² - 2x) + (6x - 3)

= x²(2x - 1) - 2x(2x - 1) + 3(2x - 1)

= (2x - 1)(x² - 2x + 3)

e) 3x³ - 14x² + 4x + 3

= 3x³ + x² - 15x² - 5x + 9x + 3

= (3x² + x²) - (15x² + 5x) + (9x + 3)

= x²(3x + 1) - 5x(3x + 1) + 3(3x + 1)

= (3x + 1)(x² - 5x + 3)

f) x³ + 5x² + 8x + 4

= x³ + x² + 4x² + 4x + 4x + 4

= (x³ + x²) + (4x² + 4x) + (4x + 4)

= x²(x + 1) + 4x(x + 1) + 4(x + 1)

= (x + 1)(x² + 4x + 4)

= (x + 1)(x + 2)²