Tìm x:
\(7x\left(x-2\right)=x-2\)
\(\Leftrightarrow7x\left(x-2\right)-\left(x-2\right)=0\)
\(\Leftrightarrow\left(x-2\right)\left(7x-1\right)=0\)
\(\Leftrightarrow\left[\begin{array}{nghiempt}x=2\\x=\frac{1}{7}\end{array}\right.\)
Phân tích đa thức thành nhân tử:
\(x^4+x^3+x+1=x^3\left(x+1\right)+\left(x+1\right)=\left(x+1\right)\left(x^3+1\right)\)
\(=\left(x+1\right)\left(x+1\right)\left(x^2-x+1\right)\)
a)\(7x\left(x-2\right)=x-2\)
\(7x^2-14x=x-2\)
\(7x^2=15x-2\\ 2=15x-7x^2\)
\(2=x\left(15-7x\right)\\ \Rightarrow x=2\)
Vậy x=2
b)\(x^4+x^3+x+1=x^3\left(x+1\right)+\left(x+1\right)=\left(x^3+1\right)\left(x+1\right)\)
\(=\left(x+1\right)\left(x^2-x+1\right)\left(x+1\right)=\left(x+1\right)^2\left(x^2-x+1\right)\)