Question

Phân tích đa thức thành nhân tử:
a) \(x^3+4x^2-29x+24\)

b) \(x^4+6x^3+7x^2-6x+1\)

Answer 1

a) nhận xét hệ số : 1 + 4 - 29 + 24 = 0

=> x³ + 4x² - 29x + 24 = x²(x-1) + 5x(x-1) - 24(x-1)

= (x-1)(x²+5x-24) = (x-1)(x-3)(x+8)

b) ...

Answer 2

a) \(x^3+4x^2-29x+24\)=\(\left(x+8\right)\left(x^2-4x+3\right)\)=\(\left(x+8\right)\left(x^2-x-3x+3\right)\)=\(\left(x+8\right)\left(x-1\right)\left(x-3\right)\)

b) \(x^4+6x^3+7x^2-6x+1\)=\(x^4+3x^3-x^2+3x^3+9x^2-3x-x^2-3x+1\)=\(x^2\left(x^2+3x-1\right)+3x\left(x^2+3x-1\right)-\left(x^2+3x-1\right)\)=\(\left(x^2+3x-1\right)\left(x^2+3x-1\right)\)=\(\left(x^2+3x-1\right)^2\)