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1) \(2x^2+5x-3=0\)
\(\Leftrightarrow2x^2+6x-x-3=0\)
\(\Leftrightarrow2x\left(x+3\right)-\left(x+3\right)=0\)
\(\Leftrightarrow\left(x+3\right)\left(2x-1\right)=0\)
\(\Rightarrow\orbr{\begin{cases}x+3=0\\2x-1=0\end{cases}\Rightarrow\orbr{\begin{cases}x=-3\\x=\frac{1}{2}\end{cases}}}\)
\(2x^2+5x-3=0\)
\(\Leftrightarrow2x^2+2x+3x-3=0\)
\(\Leftrightarrow\left(x-\frac{1}{2}\right)\left(x+3\right)=0\)
\(\Leftrightarrow\orbr{\begin{cases}x=\frac{1}{2}\\x=-3\end{cases}}\)

a,5x^2 - 10xy + 5y^2 - 20z^2
=5(x^2 -2xy +y^2-4z^2 )
=5[(x-y)^2-(2z)^2 ]
=5 .(x-y-2z)(x-y+2z)
b,.= (5x^2+5xy)-(x+y)
=5x(x+y)-(x+y)
=(x+y)(5x-1)
d,x2 - 4x + 3 = x2 - x - 3x + 3
= x(x - 1) - 3(x - 1) = (x -1)(x - 3)
e,x2 - x - 6 = x2 +2x - 3x - 6
= x(x + 2) - 3(x + 2)
= (x + 2)(x - 3)
f,x2 - x - 6 = x2 +2x - 3x - 6
= x(x + 2) - 3(x + 2)
= (x + 2)(x - 3)
g,2x^2(3x - 5)
= 2x^2 x 3x - 2x^2 x 5
= 6x^3 - 10x^2
\(\text{1) }\)
\(\text{a) }5x^2-10xy+5y^2-20z^2\)
\(=5\left(x^2-2xy+y^2-4z^2\right)\)
\(=5\left[\left(x^2-2xy+y^2\right)-4z^2\right]\)
\(=5\left[\left(x-y\right)^2-\left(2z\right)^2\right]\)
\(=5\left(x-y+2z\right)\left(x-y-2z\right)\)
\(\text{b) }5x^2+5xy-x-y\)
\(=\left(5x^2-x\right)+\left(5xy-y\right)\)
\(=x\left(5x-1\right)+y\left(5x-1\right)\)
\(=\left(5x-1\right)\left(x+y\right)\)
\(\text{c) }2\left(x+4\right)-x^2+16\)
\(=2\left(x+4\right)-\left(x^2-16\right)\)
\(=2\left(x+4\right)-\left(x+4\right)\left(x-4\right)\)
\(=\left(x+4\right)\left(2-x+4\right)\)
\(=\left(x+4\right)\left(6-x\right)\)
\(\text{d) }x^2+4x+3\)
\(=x^2+3x+x+3\)
\(=\left(x^2+3x\right)+\left(x+3\right)\)
\(=x\left(x+3\right)+\left(x+3\right)\)
\(=\left(x+3\right)\left(x+1\right)\)
\(\text{e) }x^2+5x-6\)
\(=x^2+6x-x-6\)
\(=\left(x^2+6x\right)-\left(x+6\right)\)
\(=x\left(x+6\right)-\left(x+6\right)\)
\(=\left(x+6\right)\left(x-1\right)\)

+) (5x-1). (2x+3)-3. (3x-1)=0
10x^2+15x-2x-3 - 9x+3=0
10x^2 +8x=0
2x(5x+4)=0
=> x=0 hoặc x= -4/5
+) x^3 (2x-3)-x^2 (4x^2-6x+2)=0
2x^4 -3x^3 -4x^4 + 6x^3 - 2x^2=0
-2x^4 + 3x^3-2x^2=0
x^2(-2x^2+x-2)=0
-2x^2(x-1)^2=0
=> x=0 hoặc x=1
+) x (x-1)-x^2+2x=5
x^2 -x -x^2+2x=5
x=5
+) 8 (x-2)-2 (3x-4)=25
8x - 16-6x+8=25
2x=33
x=33/2

(5x+1)(x+3)-(x-2)(5x-4)
=5x2+15x+x+3-(5x2-4x-10x+8)
=5x2+15x+x+3-5x2+4x+10x-8
=30x-5
(x^2+x-3)(x^2-x+3)
=[x2+(x-3)][x2-(x-3)]
=x2-(x-3)2
=x2-(x2-6x+9)
=x2-x2+6x-9
=6x-9

Nhầm 1 chút nhé, Bài 1 câu a) ( x^2 - 5x ) . ( x^2 - x +3) - ( x^3 - x^2 +1) . ( 2x - 1 )

(6x+1)2+(6x-1)2-2(1+6x)(6x-1)=(6x+1+1-6x)2=4
x(2x2-3)-x2(5x+1)+x2=2x3-3x-5x3-x2= -3x3-x2-3x
3x(x-2)-5x(1-x)-8(x2-3)=3x2-6x-5x+5x2-8x2+24= -11x+24
chưa chắc là đúng đâu nhé
Ta có \(x^3-x^2-5x-3=x^3+x^2-2x^2-2x-3x-3\)
\(=x^2.\left(x+1\right)-2x.\left(x+1\right)-3.\left(x+1\right)\)
\(=\left(x+1\right).\left(x^2-2x-3\right)\)
Do đó \(\left(x^3-x^2-5x-3\right):\left(x+1\right)=\left(x+1\right).\left(x^2-2x-3\right):\left(x+1\right)\)
\(=x^2-2x-3\)