\(x^3-8+2x\left(x-2\right)\)

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7 tháng 6 2021

\(x^3-8+2x\left(x-2\right)=\left(x-2\right)\left(x^2+2x+4\right)+2x\left(x-2\right)\)

\(=\left(x-2\right)\left(x^2+4x+4\right)=\left(x-2\right)\left(x+2\right)\left(x+2\right)\)

8 tháng 2 2020

(x2 - x + 1)2 - 5x(x2 - x + 1) + 4x2

Đặt x2 - x + 1 = a

<=> a2 - 5xa + 4x2 = x2 - 4xa - xa + 4x2 

 = a(a - 4x) - x(a - 4x) = (a - x)(a - 4x)

= (x2 - x + 1 - x)(x2 - x + 1 - 4x)

= (x2 - 2x + 1)(x2 - 5x + 1) = (x - 1)2(x2 - 5x + 1)

14 tháng 3 2021

Đặt x2 - x + 1 = y

đthức <=> y2 - 5xy + 4x2

= y2 - xy - 4xy + 4x2

= y( y - x ) - 4x( y - x )

= ( y - x )( y - 4x )

= ( x2 - x + 1 - x )( x2 - x + 1 - 4x )

= ( x2 - 2x + 1 )( x2 - 5x + 1 ) 

= ( x - 1 )2( x2 - 5x + 1 ) 

x^4 + y^4=(x^2)^2+(y^2)^2
=(x^2+y^2)^2-2x^2y^2
=(x^2+y^2)^2-(√2xy)^2
=(x^2+y^2-√2 xy)(x^2+y^2+√2 xy)

12 tháng 8 2020

Rút gọn:

\(P\left(x\right)=2x^2+4x\)

\(Q\left(x\right)=-x^3+2x^2-x+2\)

Để \(R\left(x\right)-P\left(x\right)-Q\left(x\right)=0\)

<=> \(R\left(x\right)=P\left(x\right)+Q\left(x\right)\)

= \(\left(2x^2+4x\right)+\left(-x^3+2x^2-x+2\right)\)

= \(-x^3+4x^2+3x+2\)

KL: \(R\left(x\right)=-x^3+4x^2+3x+2\)

24 tháng 7 2020

Bài làm:

a) \(2x^2+7x+5=\left(2x^2+2x\right)+\left(5x+5\right)=2x\left(x+1\right)+5\left(x+1\right)\)

\(=\left(2x+5\right)\left(x+1\right)\)

b) \(x^3-2x-4=\left(x^3-2x^2\right)+\left(2x^2-4x\right)+\left(2x-4\right)\)

\(=x^2\left(x-2\right)+2x\left(x-2\right)+2\left(x-2\right)=\left(x-2\right)\left(x^2+2x+2\right)\)

c) \(x^2+4x+3=\left(x^2+x\right)+\left(3x+3\right)=x\left(x+1\right)+3\left(x+1\right)\)

\(=\left(x+1\right)\left(x+3\right)\)

24 tháng 7 2020

2x2 + 7x + 5 = 2x2 + 2x + 5x + 5 = ( 2x2 + 2x ) + ( 5x + 5 ) = 2x( x + 1 ) + 5( x + 1 ) = ( 2x + 5 )( x + 1 )

x2 + 4x + 3 = x2 + x + 3x + 3 = ( x2 + x ) + ( 3x + 3 ) = x( x + 1 ) + 3( x + 1 ) = ( x + 3 )( x + 1 )

5 tháng 4 2017

Bài 1:
a) \(x^2+7x-8=x^2+2.x.\frac{7}{2}+\frac{49}{4}-\frac{81}{4}\)

\(=\left(x+\frac{7}{2}\right)^2-\frac{81}{4}=0\)

\(\Rightarrow\left(x+\frac{7}{2}\right)^2=\frac{81}{4}\)

\(\Rightarrow\orbr{\begin{cases}x+\frac{7}{2}=\frac{9}{2}\\x+\frac{7}{2}=\frac{-9}{2}\end{cases}}\Rightarrow\orbr{\begin{cases}x=1\\x=-8\end{cases}}\)

Vậy nghiệm của đa thức m(x) là 1 hoặc -8

b) \(\left(x-3\right)\left(16-4x\right)=0\)

\(\Rightarrow\orbr{\begin{cases}x-3=0\\16-4x=0\end{cases}}\Rightarrow\orbr{\begin{cases}x=3\\x=4\end{cases}}\)

Vậy nghiệm của đa thức g(x) là 3 hoặc 4

c) \(5x^2+9x+4=0\)

\(\Rightarrow x^2+\frac{9}{5}x+\frac{4}{5}=0\)

\(\Rightarrow x^2+2x.\frac{9}{10}+\frac{81}{100}-\frac{1}{100}=0\)

\(\Rightarrow\left(x+\frac{9}{10}\right)^2-\frac{1}{100}=0\)

\(\Rightarrow\left(x+\frac{9}{10}\right)^2=\frac{1}{100}\)

\(\Rightarrow\orbr{\begin{cases}x+\frac{9}{10}=\frac{1}{10}\\x+\frac{9}{10}=\frac{-1}{10}\end{cases}}\Rightarrow\orbr{\begin{cases}x=\frac{-4}{5}\\x=-1\end{cases}}\)

Vậy...

24 tháng 7 2020

a. \(x^5+x+1\)

\(=\left(x^5-x^2\right)+x^2+x+1\)

\(=x^2\left(x^3-1\right)+x^2+x+1\)

\(=x^2\left(x-1\right)\left(x^2+x+1\right)\)\(+x^2+x+1\)

\(=\left[x^2\left(x-1\right)+1\right]\left(x^2+x+1\right)\)

\(=\left(x^3-x^2+1\right)\left(x^2+x+1\right)\)

b.\(x^3+x^2+4\)

=\(x^3+2x^2-x^2-2x+2x+4\)

\(=x^2\left(x+2\right)-x\left(x+2\right)+2\left(x+2\right)\)

\(=\left(x+2\right)\left(x^2-x+2\right)\)
c.\(x^4+2x^2-24\)

\(=x^4+2x^3-2x^3-4x^2+6x^2+12x-12x-24\)

\(=x^3\left(x+2\right)-2x^2\left(x+2\right)+6x\left(x+2\right)-12\left(x+2\right)\)

\(=\left(x^3-2x^2+6x-12\right)\left(x+2\right)\)

\(=\left[x^2\left(x-2\right)+6\left(x-2\right)\right]\left(x+2\right)\)

\(=\left(x^2+6\right)\left(x-2\right)\left(x+2\right)\)

24 tháng 7 2020

a, x^5 + x + 1 = x ^ 5 - x^2 + (x ^2 + x + 1) = x^2 ( x-1) ( x^2+x+1) + ( x^2+x+1) = ( x^2+x+1 ) ( x^3-x^2+1)

c, x^4 + 2x^2 -24 = (x^4 +6x^2) - ( 4x^2+24) = x^2( x^2+6) - 4(x^2+6) = (x^2-4)(x^2 +6 ) = (x-2)(x+2)(x^2+6)

27 tháng 12 2019

\(f\left(x\right)+h\left(x\right)-g\left(x\right)\)

\(=\left(5x^4+3x^2+x-1\right)+\left(-x^4+3x^3-2x^2-x+2\right)\)

\(-\left(2x^4-x^3+x^2+2x+1\right)\)

\(=\left(5x^4-x^4-2x^4\right)+\left(3x^3+x^3\right)+\left(3x^2-2x^2-x^2\right)\)

\(+\left(x-x-2x\right)+\left(-1+2-1\right)\)

\(=2x^4+4x^3-2x\)

18 tháng 5 2017

\(M\left(x\right)+N\left(x\right)\)

\(=5x^3-x^2-4+2x^4-2x^2+2x+1\)

\(=2x^4+5x^3-3x^2+2x-3\)

\(M\left(x\right)-N\left(x\right)\)

\(=5x^3-x^2-4-\left(2x^4-2x^2+2x+1\right)\)

\(=5x^3-x^2-4-2x^4+2x^2-2x-1\)

\(=-2x^4+5x^3+x^2-2x-5\)

\(M\left(x\right)+P\left(x\right)=N\left(x\right)\)

\(\Rightarrow P\left(x\right)=N\left(x\right)-M\left(x\right)\)

\(\Rightarrow P\left(x\right)=2x^4-2x^2+2x+1-\left(5x^3-x^2-4\right)\)

\(\Rightarrow P\left(x\right)=2x^4-2x^2+2x+1-5x^3+x^2+4\)

\(\Rightarrow P\left(x\right)=2x^4-5x^3-x^2+2x+5\)

7 tháng 8 2020

\(P\left(x\right)-Q\left(x\right)=\left(-2x+\frac{1}{2}x^2+3x^4-3x^2-3\right)-\left(3x^4+x^3-4x^2+1,5x^3-3x^4+2x+1\right)\\ P\left(x\right)-Q\left(x\right)=-2x+\frac{1}{2}x^2+3x^4-3x^2-3-3x^4-x^3+4x^2-1,5x^3+3x^4-2x-1\\ P\left(x\right)-Q\left(x\right)=\left(-2x-2x\right)+\left(\frac{1}{2}x^2-3x^2+4x^2\right)+\left(3x^4-3x^4+3x^4\right)+\left(-3-1\right)+\left(-x^3-1,5x^3\right)\\ P\left(x\right)-Q\left(x\right)=-4x+\frac{3}{2}x^2+3x^4-4-\frac{5}{2}x^3\)

\(R\left(x\right)+P\left(x\right)-Q\left(x\right)+x^2=2x^3-\frac{3}{2}x+1\\ \Rightarrow R\left(x\right)+\left(P\left(x\right)-Q\left(x\right)\right)+x^2=2x^3-\frac{3}{2}x+1\\ \Rightarrow R\left(x\right)-4x+\frac{3}{2}x^2+3x^4-4-\frac{5}{2}x^3+x^2=2x^3-\frac{3}{2}x+1\\ \Rightarrow R\left(x\right)-4x+\left(\frac{3}{2}x+x^2\right)+3x^4-4-\frac{5}{2}x^3=2x^3-\frac{3}{2}x+1\\ \Rightarrow R\left(x\right)-4x+\frac{5}{2}x^2+3x^4-4-\frac{5}{2}x^3=2x^3-\frac{3}{2}x+1\\ \Rightarrow R\left(x\right)=2x^3-\frac{3}{2}x+1+4x-\frac{5}{2}x^2-3x^4+4+\frac{5}{2}x^3\\ \Rightarrow R\left(x\right)=\left(2x^3+\frac{5}{2}x^3\right)+\left(\frac{-3}{2}x+4x\right)+\left(1+4\right)-\frac{5}{2}x^2-3x^4\\ \Rightarrow R\left(x\right)=\frac{9}{2}x^3+\frac{5}{2}x+5-\frac{5}{2}x^2-3x^4\)