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7x2 - 14x = 0
7x(x - 2) = 0
\(\Leftrightarrow\orbr{\begin{cases}x=0\\x-2=0\end{cases}}\)
\(\Leftrightarrow\orbr{\begin{cases}x=0\\x=2\end{cases}}\)
b) 3x4-3x3+9x3-9x2-24x2+24x-48x+48
=3x3(x-1)+9x2(x-1)-24x(x-1)-48(x-1)
=(x-1)(3x3+9x2-24x-48)
=3(x-1)(x3+3x2-8x-16)
x4+7x3+14x2+14x+4
=x4+7x3+4x2+10x2+14x+4
=(x4+4x2+4)+(7x3+14x)+10x2
=(x2+2)2+7x(x2+2)+10x2
=(x2+2)2+2x(x2+2)+5x(x2+2)+10x2
=(x2+2)(x2+2+2x)+5x(x2+2+2x)
=(x2+2+2x)(x2+2+5x)
a, \(x^4+6x^3+7x^2-6x+1\)
\(=x^4-2x^2+1+6x^3+9x^2+6x\)
\(=\left(x^2-1\right)^2+6x\left(x^2-1\right)+9x^2\)
\(=\left(x^2-1+3x\right)^2\)
b, \(x^4-7x^3+14x^2-7x+1\)
\(=x^4+2x^2+1+7x^3+12x^2-7x\)
\(=\left(x^2+1\right)^2-7x\left(x^2+1\right)+12^2\)
\(=\left(x^2-1+3x\right)^2\)
c, \(12x^2-11x-36\)
\(=12x^2-27x+16x-36\)
\(=3x\left(4x-9\right)+4\left(4x-9\right)\)
\(=\left(4x-9\right)\left(3x+4\right)\)
\(7x^2-14x=0\\ \Leftrightarrow x^2-2x=0\\ \Leftrightarrow x^2-2x+1=1\\ \Leftrightarrow\left(x-1\right)^2=1\\ \Leftrightarrow\left[{}\begin{matrix}x-1=-1\\x-1=1\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}x=0\\x=2\end{matrix}\right.\)