Phân tích x^4+2014x^2+2015x+2016 thành nhân tử
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x4+2015x2+2014x+2015
=x4-x+2015x2+2015x+2015
=x.(x3-1)+2015.(x2+x+1)
=x.(x-1)(x2+x+1)+2015.(x2+x+1)
=(x2+x+1)(x2-x+2015)
\(x^4+2015x^2+2014x+2015=\left(x^4+x^3+x^2\right)-\left(x^3+x^2+x\right)+\left(2015x^2+2015x+2015\right)\)
\(=x^2\left(x^2+x+1\right)-x\left(x^2+x+1\right)+2015\left(x^2+x+1\right)=\left(x^2+x+1\right)\left(x^2-x+2015\right)\)
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\(x^4+2015x^2+2014x+2015\)
\(=\left(x^4-x\right)+2015x^2+2015x+2015\)
\(=x\left(x^3-1\right)+2015\left(x^2+x+1\right)\)
\(=x\left(x-1\right)\left(x^2+x+1\right)+2015\left(x^2+x+1\right)\)
\(=\left(x^2+x+1\right)\left(x^2-x+2015\right)\)
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bạn có: x^4 + 2016x^2 + 2015x + 2016
= x^4 + x^3 + x^2 - x^3 - x^2 - x + 2016x^2 + 2016x + 2016
= x^2(x^2 + x + 1) - x(x^2 + x + 1) + 2016(x^2 + x + 1)
= (x^2 + x + 1)(x^2 - x + 2016)
\(x^4+2016x^2+2015x+2016\)
=\(x^4+x^3+x^2+2015x^2+2015x+2015+1-x^3\)
=\(x^2\left(x^2+x+1\right)+2015\left(x^2+x+1\right)+\left(1-x\right)\left(x^2+x+1\right)\)
=\(\left(x^2+x+1\right)\left(x^2+2015+1-x\right)\)
=\(\left(x^2+x+1\right)\left(x^2-x+2016\right)\)
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2015x4 + 2016x2 + x + 2016
= (2015x4 + 2015x3 + 2015x2) + (- 2015x3 - 2015x2 - 2015x) + (2016x2 + 2016x + 2016)
= (x2 + x + 1)(2015x2 - 2015x + 2016)
Phân tích thành tích: x^4+2015x^2+2014x+2015
Tìm giá trị nhỏ nhất của biểu thức A =a^4-2a^3+3a^2-4a+5
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Câu 1 nha bạn
x^4 + x^3 + x^2 + 2014x^2 + 2014x + 2014 + 1 - x^3
=> x^4 + x^3 + x^2 + 2014x^2 + 2014x + 2014 - x^3 - 1
=> x^2 ( x^2 + x + 1 ) + 2014 ( x^2 + x + 1 ) - ( x - 1 )( x^2 + x + 1 )
=> ( x^2 + x + 1 )( x^2 + 2014 - x - 1)
![](https://rs.olm.vn/images/avt/0.png?1311)
Ta có: x^4 + 2016x^2 + 2015x + 2016
= x^4 + x^3 + x^2 - x^3 - x^2 - x + 2016x^2 + 2016x + 2016
= x^2(x^2 + x + 1) - x(x^2 + x + 1) + 2016(x^2 + x + 1)
= (x^2 + x + 1)(x^2 - x + 2016)
\(x^4+2016x^2+2015x+2016\)
\(=x^4-x+2016x^2+2016x+2016\)
\(=x\left(x^3-1\right)+2016\left(x^2+x+1\right)\)
\(=x\left(x-1\right)\left(x^2+x+1\right)+2016\left(x^2+x+1\right)\)
\(=\left(x^2+x+1\right)\left(x^2-x+2016\right)\)
![](https://rs.olm.vn/images/avt/0.png?1311)
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)
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)
Sửa đề: 2016x^2
x^4+2016x^2+2015x+2016
=x^4+x^3+x^2-x^3-x^2-x+2016x^2+2016x+2016
=(x^2+x+1)(x^2-x+2016)