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a,x^4+2x^3-4x-4
=(x^3+2x^3)-(4x+4)
=x^3(x+2)-4(x+2)
=(x^3-4)(x+2)
\(X^4+2X^3-4X-4\)
\(=\left(X^2\right)^2+2X^3-4X-2^2\)
\(=\left[\left(X^2\right)^2-2^2\right]+\left[2X^3-4X\right]\)
\(=\left(X^2+2\right)\left(X^2-2\right)+2X\left(X^2-2\right)\)
\(=\left(X^2-2\right)\left(X^2+2+2X\right)\)
a) 3x3-2x2+2 chia x+1= 3x2-5x+5 dư -3 b) -3 chia hết x+1 vậy chon x =2
1)
a) \(-7x\left(3x-2\right)\)
\(=-21x^2+14x\)
b) \(87^2+26.87+13^2\)
\(=87^2+2.87.13+13^2\)
\(=\left(87+13\right)^2\)
\(=100^2\)
\(=10000\)
2)
a) \(x^2-25\)
\(=x^2-5^2\)
\(=\left(x-5\right)\left(x+5\right)\)
b) \(3x\left(x+5\right)-2x-10=0\)
\(\Leftrightarrow3x\left(x+5\right)-\left(2x-10\right)=0\)
\(\Leftrightarrow3x\left(x+5\right)-2\left(x-5\right)=0\)
\(\Leftrightarrow\left(x+5\right)\left(3x-2\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x+5=0\\3x-2=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=-5\\3x=2\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=-5\\x=\dfrac{2}{3}\end{matrix}\right.\)
Vậy..........
3)
a) \(A:B=\left(3x^3-2x^2+2\right):\left(x+1\right)\)
Vậy \(\left(3x^3-2x^2+2\right):\left(x+1\right)=\left(3x^2-5x-5\right)+7\)
b)
Để \(A⋮B\Rightarrow7⋮\left(x+1\right)\)
\(\Rightarrow\left(x+1\right)\in U\left(7\right)=\left\{-1;1-7;7\right\}\)
Vì x là số nguyên nên x=0 ; x=6 thì \(A⋮B\)
1
a) x2 + 4y2 + 4xy - 16
=(x2 + 4xy + 4y2) - 16
=(x+2y)2 - 16
=(x+2y-4)(x+2y+4)
b)x2 + y2 - 2x + 4y + 5 =0
<=> x2 - 2x + 1 + y2 - 4y + 4=0
<=> (x-1)2 + (y-2)2 =0
<=> x=1 và y=2
Bài 2
\(a,x^3+2x^2+x\)
\(=x.\left(x^2+2x+1\right)\)
\(b,xy+y^2-x-y\)
\(=y.\left(x+y\right)-\left(x+y\right)\)
\(=\left(y-1\right).\left(x+y\right)\)
bài 3
\(a,3x.\left(x^2-4\right)=0\)
\(\Rightarrow\orbr{\begin{cases}3x=0\\x^2=4\end{cases}}\)
\(\Rightarrow\orbr{\begin{cases}x=0\\x=2,x=-2\end{cases}}\)
vậy x=0,x=2 hay x=-2
\(b,xy+y^2-x-y=0\)
\(y.\left(x+y\right)-\left(x+y\right)=0\)
\(\left(y-1\right).\left(x+y\right)=0\)
\(\Rightarrow\orbr{\begin{cases}y-1=0\\x+y=0\end{cases}\Rightarrow\orbr{\begin{cases}y=1\\x=-1\end{cases}}}\)
vậy x=-1, y=1
a) \(x^3-5x^2+8x-4\)
\(=x^3-2x^2-3x^2+6x+2x-4\)
\(=x^2\left(x-2\right)-3x\left(x-2\right)+2\left(x-2\right)\)
\(=\left(x-2\right)\left(x^2-3x+2\right)\)
\(=\left(x-2\right)\left(x^2-x-2x+2\right)\)
\(=\left(x-2\right)\left[x\left(x-1\right)-2\left(x-1\right)\right]\)
\(=\left(x-2\right)\left(x-1\right)\left(x-2\right)\)
b) \(A=10x^2-15x+8x-12+7\)
\(A=5x\left(2x-3\right)+4\left(2x-3\right)+7\)
\(A=\left(2x-3\right)\left(5x+4\right)+7\)
Dễ thấy \(\left(2x-3\right)\left(5x+4\right)⋮\left(2x-3\right)=B\)
Vậy để \(A⋮B\)thì \(7⋮\left(2x-3\right)\)
\(\Rightarrow2x-3\inƯ\left(7\right)=\left\{\pm1;\pm7\right\}\)
\(\Rightarrow x\in\left\{2;1;5;-2\right\}\)
Vậy.......
a) x2 + 4x + 3 - y2 -2y
= x2 +4x + 4 - y2 -2y-1
= (x+2)2 - (y+1)2
= (x+2-y-1).(x+2+y+1)
= (x-y+1).(x+y+3)
b) 2a2 -5ab + 2b2
= 2a2 -4ab + 2b2 - ab
= 2.(a2 - 2ab+b2) - ab
= 2.(a-b)2 -ab
...
c) (x+y)2 - 2x - 2y + 1
= (x+y)2 - 1 - 2x -2y +2
= (x+y-1).(x+y+1) - 2.(x+y-1)
= (x+y-1)2
\(x^4-2x^2y^2+y^4-1=0\Leftrightarrow\left(x^2-y^2\right)^2-1=0\Leftrightarrow\left(x^2-y^2-1\right).\left(x^2-y^2+1\right)=0\\ \)
\(x^2+2xy+2x+2y+y^2+1=0\Leftrightarrow\left(x+y+1\right)^2=0\)
a) -x2 + 2x - 1
= -( x2 - 2x + 1 )
= -( x - 1 )2
b) 12y - 36 - y2
= -( y2 - 12y + 36 )
= -( y - 6 )2
c) -x3 + 9x2 - 27x + 27
= -( x3 - 9x2 + 27x - 27 )
= -( x - 3 )3
d) x3 - 6x2 + 9x
= x( x2 - 6x + 9 )
= x( x - 3 )2
e) a3b - ab3
= ab( a2 - b2 )
= ab( a - b )( a + b )
f) a2 + 2a + 1 - b2
= a2 + ab + a - ab - b2 - b + a + b + 1
= a( a + b + 1 ) - b( a + b + 1 ) + 1( a + b + 1 )
= ( a - b + 1 )( a + b + 1 )
a)\(-x^2+2x-1\)
\(=-\left(x^2-2x+1\right)\)
\(=-\left(x-1\right)^2\)
b) \(12y-36-y^2\)
\(=-\left(y^2-12y+36\right)\)
\(=-\left(y^2-2\cdot1\cdot6+6^2\right)\)
\(=-\left(y-6\right)^2\)
c) \(-x^3+9x^2-27x+27\)
\(=-x^3+3x^2+6x^2-18x-9x+27\)
\(=-x^2\left(x-3\right)+6x\left(x-3\right)-9\left(x-3\right)\)
\(=\left(x-3\right)\left(-x^2+6x-9\right)\)
\(=\left(x-3\right)\cdot-\left(x^2-6x+9\right)\)
\(=\left(x-3\right)\cdot-\left(x^2-2\cdot x\cdot3+3^2\right)\)
\(=-\left(x-3\right)\left(x-3\right)^2\)
\(=\left(x-3\right)^3\)
d) \(x^3-6x^2+9\)
\(=x\left(x^2-6x+9\right)\)
\(=x\left(x-3\right)^2\)
e) \(a^3b-ab^3\)
\(=ab\left(a^2-b^2\right)\)
\(=ab\left(a-b\right)\left(a+b\right)\)
f) \(a^2+2a+1-b^2\)
\(=a^2+2\cdot a\cdot1+1^2-b^2\)
\(=\left(a+1\right)^2-b^2\)
\(=\left(a+1-b\right)\left(a+1+b\right)\)
a) \(\left(2a+b\right)^2-\left(2b+a\right)^2\)
\(=\left(2a+b+2b+a\right)\left(2a+b-2b-a\right)\)
\(=3\left(a+b\right)\left(a-b\right)\)
b) \(x^4+2x^2y+y^2\)
\(=\left(x^2+y\right)^2\)