\(x^4-x^2+1\)

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\(2x.\left(x-1\right)-\left(1-x\right)^2=0\)

\(\Rightarrow2x.\left(x-1\right)-\left(x-1\right)^2=0\)

\(\Rightarrow\left(x-1\right).[2x-\left(x-1\right)]=0\)

\(\Rightarrow\left(x-1\right).\left(2x-x+1\right)=0\)

\(\Rightarrow\left(x-1\right).\left(x+1\right)=0\)

\(\Rightarrow\orbr{\begin{cases}x-1=0\\x+1=0\end{cases}}\Rightarrow\orbr{\begin{cases}x=1\\x=-1\end{cases}}\)

A=x.(5x^2+1)-x.(4x^2+2)

=5x^3+x-4x^3-2x

=x^3+x-2x

=x^3-x

đặt phép chia:

x^3 -x x-1 x^2+x - x^3-x^2 x^2-x - x^2-x 0

=> A=(tự ghi) chia hết cho (x-1) với mọi số nguyên 

\(-x^2+x+42=0 \)

<=>\(-x^2-6x+7x+42=0 \)

<=>\(-x\left(x+6\right)+7\left(x+6\right)=0 \)

<=>\(\left(x+6\right)\left(7-x\right)=0 \)

<=>\(\orbr{\begin{cases}x+6=0\\7-x=0\end{cases}}< =>\orbr{\begin{cases}x=-6\\x=7\end{cases}}\)

(x+2)²-x²+2x-1

=(x+2)²-(x²-2x+1)

=(x+2)² - ( x-1)² 

=(x+2-x+1)(x+2+x-1)

=3(2x+1)

\(\left(x+2\right)^2-x^2+2x-1\)

\(=\left(x+2\right)^2-x^2+2x-1\)

\(=\left(x+2\right)^2-\left(x^2-2x+1\right)\)

\(=\left(x+2\right)^2-\left(x-1\right)^2\)

\(=[\left(x+2\right)-\left(x-1\right)].[\left(x+2\right)+\left(x-1\right)]\)

\(=\left(x+2+x-1\right).\left(x+2-x+1\right)\)

\(=3.\left(2x+1\right)\)