Phân tích đa thức thành nhân tử: \(x^4+2013x^2+2012x+2013\)
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NT
1
21 tháng 3 2016
x4+2013x2+2012x+2013= (x4-x)+(2013x2+2013x+2013)
=x(x3-1)+2013(x2+x+1)
=x(x-1)(x2+x+1)+2013(x2+x+1)
=(x2+x+1)(x2-x+2013)
3 tháng 5 2019
a, \(x^4+2013x^2+2012x+2013\)
\(=x^4+2013x^2-x+2013x+2013\)
\(=\left(x^4-x\right)+\left(2013x^2+2013x+2013\right)\)
\(=x\left(x^3-1\right)+2013\left(x^2+x+1\right)\)
\(=x\left(x-1\right)\left(x^2+x+1\right)+2013\left(x^2+x+1\right)\)
\(=\left(x^2+x+1\right)\left\{x\left(x-1\right)+2013\right\}\)
\(=\left(x^2+x+1\right)\left(x^2-x+2013\right)\)
L
1
23 tháng 8 2018
\(2012x^2-x-2013=0\)
\(\Rightarrow2012x^2+2012x-2013x-2013=0\)
\(\Rightarrow2012x\left(x+1\right)-2013\left(x+1\right)=0\)
\(\Rightarrow\left(2012x-2013\right)\left(x+1\right)=0\)
\(\Rightarrow\orbr{\begin{cases}2012x-2013=0\\x+1=0\end{cases}\Rightarrow\orbr{\begin{cases}x=\frac{2013}{2012}\\x=-1\end{cases}}}\)
Chúc bạn học tốt.
NP
1
15 tháng 12 2022
x4+2012x2+2012x+2012
=(x4-x)+(2012x2+2012x+2012)
=x(x3-1)+2012(x2+x+1)
=x(x-1) (x2+x+1) + 2012 (x2+x+1)
=(x2+x+1) [x(x-1)+2012]
=(x2+x+1) (x2-x+2012)
KJ
2
R
18 tháng 8 2019
x4+2012x2+2011x+2012
=(x4-x)+(2012x2+2012x+2012)
=x(x3-1)+2012(x2+x+1)
=x(x-1) (x2+x+1) + 2012 (x2+x+1)
=(x2+x+1) [x(x-1)+2012]
=(x2+x+1) (x2-x+2012)
PT
2
31 tháng 12 2014
ta có:
x^4+2014x^2+2013x+2014 = x^4+2013x^2+x^2+2013x+2013+1
=(x^4+x^2+1)+2013(x^2+x+1)
=(x^2+1)^2-x^2+2013(x^2+x+1)
=(x^2-x+1)(x^2+x+1)+2013(x^2+x+1)
=(x^2+x+1)(x^2+x+2014)
24 tháng 3 2016
x4+2014x2+2013x+2014=(x4-x)+(2014x2+2014x+2014)
=x(x-1)(x2+x+1)+2014(x2+x+1)
=(x^2+x+1)(x2-x+2014)
VT
2
1 tháng 9 2015
x^4+2014x^2+2013x+2014 = x^4+2013x^2+x^2+2013x+2013+1
=(x^4+x^2+1)+2013(x^2+x+1)
=(x^2+1)^2-x^2+2013(x^2+x+1)
=(x^2-x+1)(x^2+x+1)+2013(x^2+x+1)
=(x^2+x+1)(x^2+x+2014)
TT
1
20 tháng 8 2017
1) \(\left(x^2+3x+1\right)^2-1=\left(x^2+3x\right)\left(x^2+3x+2\right)=x\left(x+3\right)\left[\left(x^2+2x\right)+\left(x+2\right)\right]\)
\(=x\left(x+3\right)\left[x\left(x+2\right)+\left(x+2\right)\right]=x\left(x+3\right)\left(x+1\right)\left(x+2\right)\)
2) \(x^4+2012x^2+2011x+2012\)
\(=\left(x^4-x\right)+\left(2012x^2+2012x+2012\right)\)
\(=x\left(x^3-1\right)+2012\left(x^2+x+1\right)\)
\(=x\left(x-1\right)\left(x^2+x+1\right)+2012\left(x^2+x+1\right)\)
\(=\left(x^2+x+1\right)\left[x\left(x-1\right)+2012\right]\)
\(=\left(x^2+x+1\right)\left(x^2-x+2012\right)\)
x^4+2013x^2+2012x+2013
=(x^4-x)+(2013x^2+2013x+2013)
=x(x^3-1)+2013(x^2+x+1)
=x(x-1)(x^2+x+1)+2013(x^2+x+1)
=(x^2+x+1)(x^2-x+2013)
chúc bạn học tốt ^ ^
\(x^4+2013x^2+2012x+2013\)
=\(x^4+2013x^2+2013x-x+2013\)
=\(\left(x^4-x\right)+\left(2013x^2+2013x+2013\right)\)
=\(x\left(x^3-1\right)+2013\left(x^2+x+1\right)\)
=\(x\left(x-1\right)\left(x^2+x+1\right)+2013\left(x^2+x+1\right)\)
=\(\left(x^2+x+1\right)\left(x^2-x+2013\right)\)