Question

Phân tích nhân tử:

a) \(5xy^{^{ }3}\) + \(30x^2z^2\) - \(6x^3yz\) - \(25y^2z\)

b) \(x^3\) + \(9x^2\) + 26x + 24

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

Answer 1

a) \(5xy^3+30x^2z^2-6x^3yz-25y^2z\)

\(=\left(5xy^3-25y^2z\right)+\left(30x^2z^2-6x^3yz\right)\)

\(=5y^2\left(xy-5z\right)+6x^2z\left(5z-xy\right)\)

\(=5y^2\left(xy-5z\right)-6x^2z\left(xy-5z\right)\)

\(=\left(xy-5z\right)\left(5y^2-6x^2z\right)\)

P/s:Bài này chỉ có nước mỏ hạng tử để ghép -_-

Answer 2

xí câu dễ nhất (còn lại làm sau)

c): Đặt \(t=x^2-x\). Ta có:

\(\left(t+1\right)\left(t+2\right)-12=t^2+3t-10\)

\(=t^2+5t-2t-10\)

\(=t\left(t+5\right)-2\left(t+5\right)=\left(t-2\right)\left(t+5\right)\)

\(=\left(x^2-x-2\right)\left(x^2-x+5\right)\)

Answer 3

b) \(x^3+9x^2+26x+24=\left(x^3+3x^2\right)+\left(6x^2+18x\right)+\left(8x+24\right)\)

\(=x^2\left(x+3\right)+6x\left(x+3\right)+8\left(x+3\right)\)

\(=\left(x^2+6x+8\right)\left(x+3\right)=\left(x^2+2x+4x+8\right)\left(x+3\right)\)

\(=\left[x\left(x+2\right)+4\left(x+2\right)\right]\left(x+3\right)=\left(x+2\right)\left(x+3\right)\left(x+4\right)\)