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a ) \(x^3-7x-6=x^3-x-6x-6=x^3-x-6\left(x+1\right)\)
\(=x\left(x^2-1\right)-6\left(x+1\right)=\left(x+1\right)\left[x\left(x-1\right)-6\right]\)
\(=\left(x+1\right)\left[\left(x^2-x-6\right)\right]=\left(x+1\right)\left[\left(x^2+2x-3x-6\right)\right]\)
\(=\left(x+1\right)\left[x\left(x+2\right)-3\left(x+2\right)\right]=\left(x+1\right)\left(x+2\right)\left(x+3\right)\)
b )
\(x^3-19x-30=\left(x^3-9x\right)-\left(10x+30\right)=x\left(x^2-9\right)-10\left(x+3\right)\)
\(=\left(x+3\right)\left(x^2-3x-10\right)=\left(x+2\right)\left(x+3\right)\left(x-5\right)\)
c )
\(a^3-6a^2+11a-6=\left(a-3\right)\left(a-2\right)\left(a-1\right).\)
a)\(x^3-x^2-14x+24=x^3-3x^2+2x^2-6x-8x+24\)
\(=x^2\left(x-3\right)+2x\left(x-3\right)-8\left(x-3\right)\)
\(=\left(x-3\right)\left(x^2+2x-8\right)\)
=\(\left(x-3\right)\left(x^2+4x-2x-8\right)=\left(x-3\right)\left(x-2\right)\left(x+4\right)\)
b)Tương tự câu a
c)\(x^3-7x+6=x^3-x^2+x^2-x-6x+6\)
=\(x^2\left(x-1\right)+x\left(x-1\right)-6\left(x+1\right)=\left(x+1\right)\left(x^2+x-6\right)\)
=\(\left(x+1\right)\left(x^2+3x-2x-6\right)\)
=\(\left(x+1\right)\left(x-2\right)\left(x+3\right)\)
d;e thương tự câu c
\(x^3+4x^2+4x+3\)
\(=\left(x^3+3x^2\right)+\left(x^2+3x\right)+\left(x+3\right)\)
\(=\left(x+3\right)\left(x^2+x+1\right)\)
mình làm 1 câu còn câu còn lại bạn tự làm nha giờ mình bận
a) \(a^4+6a^2+11a+6\)
\(=a^3+a^2+5a^2+5a+6a+6\)
\(=a^2\left(a+1\right)+5a\left(a+1\right)+6\left(a+1\right)\)
\(=\left(a^2+5a+6\right)\left(a+1\right)\)
\(=\left(a^2+2a+3a+6\right)\left(a+1\right)\)
\(=\left[a\left(a+2\right)+3\left(a+2\right)\right]\left(a+1\right)\)
\(=\left(x+2\right)\left(x+3\right)\left(x+1\right)\)
\(a,x\left(x-3\right)=x^2-6\\ \Rightarrow x^2-3x-x^2=-6\\ \Rightarrow-3x=-6\\ \Rightarrow x=2\\ b,x^2-7x+12=0\\ \Rightarrow\left(x^2-3x\right)-\left(4x-12\right)=0\\ \Rightarrow x\left(x-3\right)-4\left(x-3\right)=0\\ \Rightarrow\left(x-3\right)\left(x-4\right)=0\\ \Rightarrow\left[{}\begin{matrix}x=3\\x=4\end{matrix}\right.\\ d,x^3-25x=0\\ \Rightarrow x\left(x^2-25\right)=0\\ \Rightarrow x\left(x-5\right)\left(x+5\right)=0\\ \Rightarrow\left[{}\begin{matrix}x0=\\x=5\\x=-5\end{matrix}\right.\)
a) \(x^3-7x-6\)
\(=\left(x^3+2x^2\right)-\left(2x^2+4x\right)-\left(3x+6\right)\)
\(=\left(x+2\right)\left(x^2-2x-3\right)\)
\(=\left(x+2\right)\left(x-3\right)\left(x+1\right)\)
b)\(x^3-19x-30\)
\(=\left(x^3-5x^2\right)+\left(5x^2-25x\right)+\left(6x-30\right)\)
\(=\left(x-5\right)\left(x^2+5x+6\right)\)
\(=\left(x-5\right)\left(x+2\right)\left(x+3\right)\)
c) \(a^3-6a^2+11a-6\)
\(=\left(a^3-a^2\right)-\left(5a^2-5a\right)+\left(6a-6\right)\)
\(=\left(a-1\right)\left(a^2-5a+6\right)\)
\(=\left(a-1\right)\left(a-2\right)\left(a-3\right)\)