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\(=x^2\left(8x-3\right)-\left(8x-3\right)=\left(8x-3\right)\left(x^2-1\right)\)
\(a,x^3+y^3+z^3-3xyz\)
\(=\left(x+y+z\right)\left[\left(x+y\right)^2-\left(x+y\right)z+z^2\right]-3xy\left(x+y+z\right)\)
\(=\left(x+y+z\right)\left(x^2+y^2+z^2+2xy-xz-yz\right)-3xy\left(x+y+z\right)\)
\(=\left(x+y+z\right)\left(x^2+y^2+z^2-xy-yz-xz\right)\)
b) \(f\left(x\right)=12x^3-32x^2+25x-6\)
Thấy \(x=\frac{3}{2}\) là một nghiệm.Vậy đa thức có chứa nhân tử \(\left(x-\frac{3}{2}\right)\)
Ta có: \(f\left(x\right)=\left(x-\frac{3}{2}\right)\left(\frac{12x^3-32x^2+25x-6}{x-\frac{3}{2}}\right)\)
\(=\left(x-\frac{3}{2}\right)\left(12x^2-14x+4\right)\)
\(=\left(x-\frac{3}{2}\right)\left[\left(12x^2-6x\right)-\left(8x-4\right)\right]\)
\(=\left(x-\frac{3}{2}\right)\left(x-\frac{2}{3}\right)\left(12x-6\right)\)
\(=12\left(x-\frac{3}{2}\right)\left(x-\frac{2}{3}\right)\left(x-\frac{1}{2}\right)\)
Ta có:\(25x^2-y^2+6yz-9z^2=25x^2-\left(y-3z\right)^2=\left(5x+y-3z\right)\left(5x-y+3z\right)\)
\(25x^2-y+6yz-9z^2\)
\(=\left(5x\right)^2-\left(y^2-6yz+9z^2\right)\)
\(=\left(5x\right)^2-\left(y-3z\right)^2\)
\(=\left(5x-y+3z\right)\left(5x+y-3z\right)\)
Vậy \(25x^2-y^2+6yz-9z^2=\left(5x-y+3z\right)\left(5x+y-3z\right)\)
1.
\(\left(12x^2+6x\right)\left(y+z\right)+\left(12x^2+6x\right)\left(y-z\right)\\ =\left(12x^2+6x\right)\left(y+z+y-z\right)\\ =2y\left(12x^2+6x\right)\\ =2y.6x\left(2x+1\right)\\ =12xy\left(2x+1\right)\)
2.
\(x\left(x-6\right)+10\left(x-6\right)=0\\ \Leftrightarrow\left(x-6\right)\left(x+10\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=6\\x=-10\end{matrix}\right.\)
Vậy \(x\in\left\{6;-10\right\}\) là nghiệm của pt
Bài 1:
Ta có: \(\left(12x^2+6x\right)\left(y+z\right)+\left(12x^2+6x\right)\left(y-z\right)\)
\(=\left(12x^2+6x\right)\left(y+z+y-z\right)\)
\(=6x\left(2x+1\right)\cdot2y\)
\(=12xy\left(2x+1\right)\)
Bài 2:
Ta có: \(x\left(x-6\right)+10\left(x-6\right)=0\)
\(\Leftrightarrow\left(x-6\right)\left(x+10\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=6\\x=-10\end{matrix}\right.\)
12x2 - 32x2 +25x -6
= x ( 12x - 32x + 25 - 6 )
= x ( -20x + 19 )
bị sai đề đúng không?????????
k cho mk mấy cái đi a...hi..hi...