1.phân tích các đa thức sau thành nhân tử :
a) 5x - 15y
b) 3/5 x2 + 5x4 - x2y
c) 14x2y2 +28x2y
d)2/7x(3y - 1) - 2/7(3y - 1)
e) x3 - 3x2 + 3x - 1
f)( x+ y)2 - 4x2
g) 27x3 + 1/8
h)( x+y)3 - ( x - y)3
2. tìm x, biết:
a) x2( x + 1)+ 2x( x + 1) = 0
b) 4/9 - 25x2 = 0
c) x(3x - 2) - 5(2 -3x) = 0
d) x2 - x + 1/4 = 0
a) 5x-15y=5x-3.5.y=5(x-3y)
c) 14xy(xy+28x)
d) \(\dfrac{2}{7}\left(3x-1\right)\left(x-1\right)\)
e) (x-1)3
f) (x+y-2x)(x+y+2x)=(y-x)(3x+y)
g) (3x+\(\dfrac{1}{2}\))(9x2+\(\dfrac{3}{2}x\)+\(\dfrac{1}{4}\))
h) (x+y-x+y)\(\left[\left(x+y\right)^2-\left(x+y\right)\left(x-y\right)+\left(x-y\right)^2\right]\)
2a)
(x+1)(x2+2x)=0
(x+1)x(x+2)=0
\(\left[{}\begin{matrix}x+1=0\\x=0\\x+2=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-1\\x=0\\x=-2\end{matrix}\right.\)
2b)
\(\left(\dfrac{2}{3}\right)^2-\left(5x\right)^2=0\)
\(\Leftrightarrow\)(\(\dfrac{2}{3}-5x\))(\(\dfrac{2}{3}+5x\))=0
\(\Leftrightarrow\)\(\left[{}\begin{matrix}\dfrac{2}{3}-5x=0\\\dfrac{2}{3}+5x=0\end{matrix}\right.\)
\(\Leftrightarrow\)\(\left[{}\begin{matrix}x=\dfrac{2}{15}\\x=-\dfrac{2}{15}\end{matrix}\right.\)
2c)
x(3x-2)+5(3x-2)=0
\(\Leftrightarrow\)(3x-2)(x+5)=0
\(\Leftrightarrow\)\(\left[{}\begin{matrix}3x-2=0\\x+5=0\end{matrix}\right.\)
\(\Leftrightarrow\)\(\left[{}\begin{matrix}x=\dfrac{2}{3}\\x=-5\end{matrix}\right.\)
2d)
x2-2.x.\(\dfrac{1}{2}\)+\(\left(\dfrac{1}{2}\right)^2\)=0
\(\Leftrightarrow\)(x-\(\dfrac{1}{2}\))2=0
\(\Leftrightarrow\)x=\(\dfrac{1}{2}\)
Bổ sung bài 2 :
a ) \(x^2\left(x+1\right)+2x\left(x+1\right)=0\)
\(\Leftrightarrow\left(x+1\right)\left(x^2+2x\right)=0\)
\(\Leftrightarrow x\left(x+1\right)\left(x+2\right)=0\)
\(\Leftrightarrow\left\{{}\begin{matrix}x=0\\x+1=0\\x+2=0\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}\\x=-1\\x=-2\end{matrix}\right.\)
Vậy \(x=0;x=-1;x=-2\)
b ) \(\dfrac{4}{9}-25x^2=0\)
\(\Leftrightarrow\left(\dfrac{2}{3}\right)^2-\left(5x\right)^2=0\)
\(\Leftrightarrow\left(\dfrac{2}{3}-5x\right)\left(\dfrac{2}{3}+5x\right)=0\)
\(\Leftrightarrow\left\{{}\begin{matrix}\dfrac{2}{3}-5x=0\\\dfrac{2}{3}+5x=0\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x=\dfrac{2}{15}\\x=-\dfrac{2}{15}\end{matrix}\right.\)
Vậy \(x=\dfrac{2}{15};x=-\dfrac{2}{15}\)
c ) \(x\left(3x-2\right)-5\left(2-3x\right)=0\)
\(\Leftrightarrow x\left(3x-2\right)+5\left(3x-2\right)=0\)
\(\Leftrightarrow\left(3x-2\right)\left(x+5\right)=0\)
\(\Leftrightarrow\left\{{}\begin{matrix}3x-2=0\\x+5=0\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x=\dfrac{2}{3}\\x=-5\end{matrix}\right.\)
Vậy \(x=\dfrac{2}{3}\) và \(x=-5\)
d ) \(x^2-x+\dfrac{1}{4}=0\)
\(\Leftrightarrow\left(x-\dfrac{1}{2}\right)^2=0\)
\(\Rightarrow x=\dfrac{1}{2}\)
Vậy \(x=\dfrac{1}{2}\)