phân tích đa thức thành nhân tử (x+1)(x+2)(x+3)(x+4)-12
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12 tháng 10 2021
\(1,\\ a,=4\left(x-2\right)^2+y\left(x-2\right)=\left(4x-8+y\right)\left(x-2\right)\\ b,=3a^2\left(x-y\right)+ab\left(x-y\right)=a\left(3a+b\right)\left(x-y\right)\\ 2,\\ a,=\left(x-y\right)\left[x\left(x-y\right)^2-y-y^2\right]\\ =\left(x-y\right)\left(x^3-2x^2y+xy^2-y-y^2\right)\\ b,=2ax^2\left(x+3\right)+6a\left(x+3\right)\\ =2a\left(x^2+3\right)\left(x+3\right)\\ 3,\\ a,=xy\left(x-y\right)-3\left(x-y\right)=\left(xy-3\right)\left(x-y\right)\\ b,Sửa:3ax^2+3bx^2+ax+bx+5a+5b\\ =3x^2\left(a+b\right)+x\left(a+b\right)+5\left(a+b\right)\\ =\left(3x^2+x+5\right)\left(a+b\right)\\ 4,\\ A=\left(b+3\right)\left(a-b\right)\\ A=\left(1997+3\right)\left(2003-1997\right)=2000\cdot6=12000\\ 5,\\ a,\Leftrightarrow\left(x-2017\right)\left(8x-2\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=2017\\x=\dfrac{1}{4}\end{matrix}\right.\\ b,\Leftrightarrow\left(x-1\right)\left(x^2-16\right)=0\Leftrightarrow\left[{}\begin{matrix}x=1\\x=4\\x=-4\end{matrix}\right.\)
T
5 tháng 7 2019
#)Giải :
\(x^3-2x-4\)
\(=x^3+2x^2-2x^2+2x-4x-4\)
\(=x^3+2x^2+2x-2x^2-4x-4\)
\(=x\left(x^2+2x+2\right)-2\left(x^2+2x+2\right)\)
\(=\left(x-2\right)\left(x^2+2x+2\right)\)
\(x^4+2x^3+5x^2+4x-12\)
\(=x^4+x^3+6x^2+x^3+x^2+6x-2x^2-2x-12\)
\(=x^2\left(x^2+x+6\right)+x\left(x^2+x+6\right)-2\left(x^2+x+6\right)\)
\(=\left(x^2+x+6\right)\left(x^2+x-2\right)\)
\(=\left(x^2+x+6\right)\left(x-1\right)\left(x+2\right)\)
5 tháng 7 2019
Câu 1.
Đoán được nghiệm là 2.Ta giải như sau:
\(x^3-2x-4\)
\(=x^3-2x^2+2x^2-4x+2x-4\)
\(=x^2\left(x-2\right)+2x\left(x-2\right)+2\left(x-2\right)\)
\(=\left(x-2\right)\left(x^2+2x+2\right)\)
N
3
17 tháng 9 2020
a) ( x + 1 )( x + 2 )( x + 3 )( x + 4 ) - 15
= [ ( x + 1 )( x + 4 ) ][ ( x + 2 )( x + 3 ) ] - 15
= ( x2 + 5x + 4 )( x2 + 5x + 6 ) - 15 (*)
Đặt t = x2 + 5x + 4
(*) trở thành
t( t + 2 ) - 15
= t2 + 2t - 15
= t2 - 3t + 5t - 15
= t( t - 3 ) + 5( t - 3 )
= ( t - 3 )( t + 5 )
= ( x2 + 5x + 4 - 3 )( x2 + 5x + 4 + 5 )
= ( x2 + 5x + 1 )( x2 + 5x + 9 )
b) ( x + 2 )( x + 3 )2( x + 4 ) - 12
= [ ( x + 2 )( x + 4 ) ]( x + 3 )2 - 12
= ( x2 + 6x + 8 )( x2 + 6x + 9 ) - 12 (*)
Đặt t = x2 + 6x + 8
(*) trở thành
t( t + 1 ) - 12
= t2 + t - 12
= t2 - 3t + 4t - 12
= t( t - 3 ) + 4( t - 3 )
= ( t - 3 )( t + 4 )
= ( x2 + 6x + 8 - 3 )( x2 + 6x + 8 + 4 )
= ( x2 + 6x + 5 )( x2 + 6x + 12 )
= ( x2 + x + 5x + 5 )( x2 + 6x + 12 )
= [ x( x + 1 ) + 5( x + 1 ) ]( x2 + 6x + 12 )
= ( x + 1 )( x + 5 )( x2 + 6x + 12 )
G
17 tháng 9 2020
a, Gọi\(A=\left(x+1\right)\left(x+2\right)\left(x+3\right)\left(x+4\right)-15\)
\(=\left(x^2+5x+4\right)\left(x^2+5x+6\right)-15\)
Đặt\(y=x^2+5x+4\)
\(\Rightarrow A=y\left(y+2\right)-15\)
\(=y^2+2y-15\)
\(=\left(x-3\right)\left(x+5\right)\)
Hay\(A=\left(x^2+5x+1\right)\left(x^2+5x+9\right)\)
Vậy...
b,Gọi\(B=\left(x+2\right)\left(x+3\right)^2\left(x+4\right)-12\)
\(=\left(x^2+6x+8\right)\left(x^2+6x+9\right)-12\)
Đặt\(z=x^2+6x+8\)
\(\Rightarrow B=z\left(z+1\right)-12\)
\(=z^2+z-12\)
\(=\left(z-3\right)\left(z+4\right)\)
Hay\(B=\left(x^2+6x+5\right)\left(x^2+6x+12\right)\)
Vậy...
Linz
6 tháng 11 2021
\(1,=x\left(x^2-2x+1-y^2\right)=x\left[\left(x-1\right)^2-y^2\right]=x\left(x-y-1\right)\left(x+y-1\right)\\ 2,=\left(x+y\right)^3\\ 3,=\left(2y-z\right)\left(4x+7y\right)\\ 4,=\left(x+2\right)^2\\ 5,Sửa:x\left(x-2\right)-x+2=0\\ \Leftrightarrow\left(x-2\right)\left(x-1\right)=0\Leftrightarrow\left[{}\begin{matrix}x=1\\x=2\end{matrix}\right.\)
24 tháng 9 2021
\(1,\\ 1,=15\left(x+y\right)\\ 2,=4\left(2x-3y\right)\\ 3,=x\left(y-1\right)\\ 4,=2x\left(2x-3\right)\\ 2,\\ 1,=\left(x+y\right)\left(2-5a\right)\\ 2,=\left(x-5\right)\left(a^2-3\right)\\ 3,=\left(a-b\right)\left(4x+6xy\right)=2x\left(2+3y\right)\left(a-b\right)\\ 4,=\left(x-1\right)\left(3x+5\right)\\ 3,\\ A=13\left(87+12+1\right)=13\cdot100=1300\\ B=\left(x-3\right)\left(2x+y\right)=\left(13-3\right)\left(26+4\right)=10\cdot30=300\\ 4,\\ 1,\Rightarrow\left(x-5\right)\left(x-2\right)=0\Rightarrow\left[{}\begin{matrix}x=2\\x=5\end{matrix}\right.\\ 2,\Rightarrow\left(x-7\right)\left(x+2\right)=0\Rightarrow\left[{}\begin{matrix}x=7\\x=-2\end{matrix}\right.\\ 3,\Rightarrow\left(3x-1\right)\left(x-4\right)=0\Rightarrow\left[{}\begin{matrix}x=\dfrac{1}{3}\\x=4\end{matrix}\right.\\ 4,\Rightarrow\left(2x+3\right)\left(2x-1\right)=0\\ \Rightarrow\left[{}\begin{matrix}x=-\dfrac{3}{2}\\x=\dfrac{1}{2}\end{matrix}\right.\)
VT
2
PA
9 tháng 10 2016
\(\left(x-1\right)\left(x-2\right)\left(x-3\right)\left(x-4\right)-80=\left(x^2-5x+4\right)\left(x^2-5x+6\right)-80\)
Đặt \(x^2-5x+4=t\), ta có:
\(t\left(t+2\right)-80=t^2-2t+1-81=\left(t-1\right)^2-9^2=\left(t-1-9\right)\left(t-1+9\right)=\left(t-10\right)\left(t+8\right)\)
\(=\left(x^2-5x+4-10\right)\left(x^2-5x+4+8\right)=\left(x^2-5x-6\right)\left(x^2-5x+12\right)\)
\(\left(x^2+x+1\right)\left(x^2+x+2\right)-12\)
Đặt x2 + x + 1 = t, ta có:
t(t + 1) - 12
= t2 + t + 1/4 - 49/4
= (t + 1/2)2 - (7/2)2
= (t + 1/2 + 7/2)(t + 1/2 - 7/2)
= (t + 4)(t - 3)
ND
9 tháng 10 2016
nhân váo như bình thường sau đó bấm máy tính shift solve =? rồi chia hoocne
19 tháng 7 2021
a) \(x^3+9x^2+27x+27=\left(x+3\right)^3\)
b) \(3\sqrt{3x^3}+18x^2+12\sqrt{3x}+8=\left(\sqrt{3x}+2\right)^3\)
c) \(\dfrac{1}{4}-x^2=\left(\dfrac{1}{2}-x\right)\left(\dfrac{1}{2}+x\right)\)
TN
1
1 tháng 7 2021
Ta có: \(\left(x^2+x+1\right)\left(x^2+x+2\right)-12\)
\(=\left(x^2+x\right)^2+3\left(x^2+x\right)+2-12\)
\(=\left(x^2+x\right)^2+3\left(x^2+x\right)-10\)
\(=\left(x^2+x+5\right)\left(x^2+x-2\right)\)
\(=\left(x^2+x+5\right)\left(x+2\right)\left(x-1\right)\)
\(=\left(x+1\right)\left(x+4\right)\left(x+2\right)\left(x+3\right)-12\)
\(=\left(x^2+5x+4\right)\left(x^2+5x+6\right)-12\)
Đăt \(a=x^2+5x+5\)
\(\Rightarrow x^2+5x+5=a-1\)(Trừ 1 cho 2 vế \(a=x^2+5x+5\))
\(\Rightarrow x^2+5x+6=a+1\)( Cộng 1 vào cả 2 vế \(a=x^2+5x+5\))
\(\Rightarrow\left(x^2+5x+4\right)\left(x^2+5x+6\right)-12=\left(a-1\right)\left(a+1\right)-12\)
\(=a^2-13\)
\(= \left(a-\sqrt{13}\right)\left(a+\sqrt{13}\right)\)
\(=\left(x^2+5x+5-\sqrt{13}\right)\left(x^2+5x+5+\sqrt{13}\right)\)