a) \(x^3-7x+6=\left(x^3-2x^2\right)+\left(2x^2-4x\right)-\left(3x-6\right)\)
= \(x^2\left(x-2\right)+2x\left(x-2\right)-3\left(x-2\right)\)
= \(\left(x-2\right)\left(x^2+2x-3\right)\)
= \(\left(x-2\right)\left(x^2-x+3x-3\right)\)
= \(\left(x-2\right)\left[x\left(x-1\right)+3\left(x-1\right)\right]\)
= \(\left(x-2\right)\left(x-1\right)\left(x+3\right)\)
b) Sửa cái đề nha!
\(x^3+5x^2+8x+4\) = \(\left(x^2+2x^2\right)+\left(3x^2+6x\right)+\left(2x+4\right)\)
= \(x^2\left(x+2\right)+3x\left(x+2\right)+2\left(x+2\right)\)
= \(\left(x+2\right)\left(x^2+x+2x+2\right)\)
= \(\left(x+2\right)\left[x\left(x+1\right)+2\left(x+1\right)\right]\)
= \(\left(x+2\right)^2\left(x+1\right)\)
- Tây Nam Á có thể trồng lúa mì, bông, trồng chà là, chăn nuôi cừu ở các cao nguyên do khí hậu khô hạn. - Công nghiệp khai thác và chế biến dầu mỏ phát triển vì đây là khu vực có trữ lượng dầu khí lớn. - Phát triển dịch vụ: giao thông, du lịch do vị trí địa lí nằm thông thương giữa hai đại dương lớn qua biển Đỏ và Địa Trung Hải.
\(a,x^3-7x+6\Leftrightarrow x^3-x-6x+6\Leftrightarrow x\left(x^2-1\right)-6\left(x-1\right)\Leftrightarrow x\left(x+1\right)\left(x-1\right)-6\left(x-1\right)\Leftrightarrow\left(x-1\right)\left(x^2+x-6\right)\)\(c,x^3-9x^2+6x+16\Leftrightarrow\left(x^3-8x^2\right)-\left(x^2-8x\right)-\left(2x+16\right)\Leftrightarrow x^2\left(x-8\right)-x\left(x-8\right)-2\left(x-8\right)\Leftrightarrow\left(x-8\right)\left(x^2-x-2\right)\)
a, \(x^3-7x+6\)
\(=x^3-2x^2+2x^2-4x-3x+6\)
\(=x^2\left(x-2\right)-2x\left(x-2\right)-3\left(x-2\right)\)
\(=\left(x^2-2x-3\right)\left(x-2\right)\)
b, sai đề không bạn?
d, \(x^3-x^2-x-2\)
\(=x^3-2x^2+x^2-2x+x-2\)
\(=x^2\left(x-2\right)+x\left(x-2\right)+\left(x-2\right)\)
\(=\left(x^2+x+1\right)\left(x-2\right)\)
e, \(x^3+x^2-x+2\)
\(=x^3+2x^2-x^2-2x+x+2\)
\(=x^2\left(x+2\right)-x\left(x+2\right)+\left(x+2\right)\)
\(\left(x^2-x+1\right)\left(x+2\right)\)
c) \(x^3-9x^2+6x+16=\left(x^3-8x^2\right)-\left(x^2-8x\right)-\left(2x-16\right)\)
= \(x^2\left(x-8\right)+x\left(x-8\right)-2\left(x-8\right)\)
= \(\left(x-8\right)\left(x^2-x-2\right)\)
= \(\left(x-8\right)\left(x^2+x-2x-2\right)\)
= \(\left(x-8\right)\left[x\left(x+1\right)-2\left(x+1\right)\right]\)
= \(\left(x-8\right)\left(x+1\right)\left(x-2\right)\)
d) \(x^3-x^2-x-2=\left(x^3-2x^2\right)+\left(x^2-2x\right)+\left(x-2\right)\)
= \(x^2\left(x-2\right)+x\left(x-2\right)+\left(x-2\right)\)
= \(\left(x-2\right)\left(x^2+x+1\right)\)
e) \(x^3+x^2-x+2=\left(x^3+2x^2\right)-\left(x^2+2x\right)+\left(x+2\right)\)
= \(x^2\left(x+2\right)-x\left(x+2\right)+\left(x+2\right)\)
= \(\left(x+2\right)\left(x^2-x+1\right)\)
f) \(x^3-6x^2-x+30=\left(x^3-5x^2\right)-\left(x^2-5x\right)-\left(6x-30\right)\)
= \(x^2\left(x-5\right)-x\left(x-5\right)-6\left(x-5\right)\)
= \(\left(x-5\right)\left(x^2-x-6\right)\)
= \(\left(x-5\right)\left[x\left(x-3\right)+2\left(x-3\right)\right]\)
= \(\left(x-5\right)\left(x-3\right)\left(x+2\right)\)
