Factor f(x) = x⁴ - 2x³ - 13x² + 38x - 24 fully.?

Question

Factor f(x) = x⁴ - 2x³ - 13x² + 38x - 24 fully.?

Answer 1

= x⁴ - 2x³ - 13x² + 38x - 24



= x⁴ - (x³ + x³) - (14x² - x²) + (24x + 14x) - 24



= x⁴ - x³ - x³ - 14x² + x² + 24x + 14x - 24



= x⁴ - x³ - 14x² + 24x - x³ + x² + 14x - 24



= [x⁴ - x³ - 14x² + 24x] - [x³ - x² - 14x + 24]



= x.[x³ - x² - 14x + 24] - [x³ - x² - 14x + 24]



= (x - 1).[x³ - x² - 14x + 24]



= (x - 1).[x³ - (2x² - x²) - (12x + 2x) + 24]



= (x - 1).[x³ - 2x² + x² - 12x - 2x + 24]



= (x - 1).[x³ + x² - 12x - 2x² - 2x + 24]



= (x - 1).[(x³ + x² - 12x) - (2x² + 2x - 24)]



= (x - 1).[x.(x² + x - 12) - 2.(x² + x - 12)]



= (x - 1).[(x - 2).(x² + x - 12)]



= (x - 1).(x - 2).[x² + x - 12



= (x - 1).(x - 2).[x² + (4x - 3x) - 12]



= (x - 1).(x - 2).[x² + 4x - 3x - 12]



= (x - 1).(x - 2).[(x² + 4x) - (3x + 12)]



= (x - 1).(x - 2).[x.(x + 4) - 3.(x + 4)]



= (x - 1).(x - 2).[(x + 4).(x - 3)]



= (x - 1).(x - 2).(x + 4).(x - 3)

Answer 2

1^4 -2*1^3-13*1^2+38*1-24=0

(x-1)(x^3-x^2-14x+24)

2^3-2^2-14*2+24=0

(x-1)(x-2)(x^2+x-12)

(x-1)(x-2)(x-3)(x+4)

Answer 3

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