thực hiện phép tính :
b ( x + 2 ) ( x^2 - 2x + 4 )
c ( 4x^ - 8x^2 + 13x - 5 ) : ( 2x -1 )
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a: \(=\dfrac{2x^4+x^3-5x^2-3x-3}{x^2-3}\)
\(=\dfrac{2x^4-6x^2+x^3-3x+x^2-3}{x^2-3}\)
\(=2x^2+x+1\)
b: \(=\dfrac{x^5+x^2+x^3+1}{x^3+1}=x^2+1\)
c: \(=\dfrac{2x^3-x^2-x+6x^2-3x-3+2x+6}{2x^2-x-1}\)
\(=x+3+\dfrac{2x+6}{2x^2-x-1}\)
d: \(=\dfrac{3x^4-8x^3-10x^2+8x-5}{3x^2-2x+1}\)
\(=\dfrac{3x^4-2x^3+x^2-6x^3+4x^2-2x-15x^2+10x-5}{3x^2-2x+1}\)
\(=x^2-2x-5\)
Bài 2:
a: \(\Leftrightarrow\left(x-2\right)\left(x+1\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=2\\x=-1\end{matrix}\right.\)
a: \(=\dfrac{x^2-5x+x+4}{x\left(x-2\right)}=\dfrac{x^2-4x+4}{x\left(x-2\right)}=\dfrac{x-2}{x}\)
b: \(=\dfrac{x^2-6x+9+4x^2+8x-4x^2-8x}{\left(x-3\right)\left(x+2\right)}\)
\(=\dfrac{x-3}{x+2}\)
a) \(=\dfrac{x\left(x-5\right)+x+4}{x\left(x-2\right)}=\dfrac{x^2-4x+4}{x\left(x-2\right)}=\dfrac{\left(x-2\right)^2}{x\left(x-2\right)}=\dfrac{x-2}{x}\)
b) \(=\dfrac{\left(x-3\right)^2+4x\left(x+2\right)-8x-4x^2}{\left(x+2\right)\left(x-3\right)}=\dfrac{x^2-6x+9+4x^2+8x-8x-4x^2}{\left(x+2\right)\left(x-3\right)}\)
\(=\dfrac{x^2-6x+9}{\left(x+2\right)\left(x-3\right)}=\dfrac{\left(x-3\right)^2}{\left(x+2\right)\left(x-3\right)}=\dfrac{x-3}{x+2}\)
b. (x + 2)(x2 - 2x + 4)
= x3 - 2x2 + 4x + 2x2 - 4x + 8
= x3 + 8
c: \(\dfrac{4x^3-8x^2+13x-5}{2x-1}=\dfrac{4x^3-2x^2-6x^2+3x+10x-5}{2x-1}\)
=2x^2-3x+5