`@` `\text {dnammv}`

`a,`

`M(x)=3x^3+x^2+4x^4-x-3x^3+5x^4+x^2`

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

`= 9x^4+2x^2-x`

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

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

`= -x^4-x^3-2x^2+4x+1`

`b,`

`M(x)+N(x)=(9x^4+2x^2-x)+(-x^4-x^3-2x^2+4x+1)`

`= 9x^4+2x^2-x-x^4-x^3-2x^2+4x+1`

`= (9x^4-x^4)-x^3+(2x^2-2x^2)+(-x+4x)+1`

`= 8x^4-x^3+3x+1`

`N(x)-M(x)=(-x^4-x^3-2x^2+4x+1)-(9x^4+2x^2-x)`

`= -x^4-x^3-2x^2+4x+1-9x^4-2x^2+x`

`= (-x^4-9x^4)-x^3+(-2x^2-2x^2)+(4x+x)+1`

`= -10x^4-x^3-4x^2+5x+1`

`c,`

`P(x)=M(x)+N(x)`

`P(x)= 8x^4-x^3+3x+1`

Thay `x=-2`

`P(-2)= 8*(-2)^4-(-2)^3+3*(-2)+1`

`= 8*16+8-6+1`

`= 136-6+1=131`

a: \(M\left(x\right)=9x^4+2x^2-x-6\)

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

b: \(P\left(x\right)=8x^4-x^3+3x-5\)

\(Q\left(x\right)=10x^4+x^3+4x^2-5x-7\)

`P(x)=x^2+5x^4-3x^2+x^2+4x^4+3x^3-x+5`

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

`=9x^4+3x^3-x^2-x-5`

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

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

`=-x^4-x^3+4x-1`

`P(x)+Q(x)=9x^4+3x^3-x^2-x-5-x^4-x^3+4x-1`

`=(9x^4-x^4)+(3x^3-x^3)-x^2-(x-4x)-(5+1)`

`=8x^4+2x^3-x^2-5x-6`

`P(x)-Q(x)=9x^4+3x^3-x^2-x-5+x^4+x^3-4x+1`

`=(9x^4+x^4)+(3x^3+x^3)-x^2-(x+4x)-(5-1)`

`=10x^4+4x^3-x^2-5x-4`

a: \(M\left(x\right)=9x^4+2x^2-x-6\)

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

b: \(P\left(x\right)=8x^4-x^3+3x-5\)

\(Q\left(x\right)=10x^4+x^3+4x^2-5x-7\)

ko bt làm=))

a) Ta có: \(M\left(x\right)=3x^3+x^2+4x^4-x-3x^3+5x^4+2x^2-6\)

\(=\left(4x^4+5x^4\right)+\left(3x^3-3x^3\right)+\left(x^2+2x^2\right)-x-6\)

\(=9x^4+3x^2-x-6\)

Ta có: \(N\left(x\right)=-2x^2-x^4+4x^3-x^2-5x^3+3x+5+x\)

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

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

c) Ta có: M(x)+N(x)

\(=9x^4+3x^2-x-6-x^4-x^3-3x^2+4x+5\)

\(=8x^4-x^3+3x-1\)

a) Thu gọn và sắp xếp:

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

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

\(P\left(x\right)=9x^4+2x^2-x+5\)

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

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

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

b) \(P\left(x\right)+Q\left(x\right)\)

\(=\left(9x^4+2x^2-x+5\right)+\left(x^4-x^3-2x^2+4x-1\right)\)

\(=9x^4+2x^2-x+5+x^4-x^3-2x^2+4x-1\)

\(=\left(9x^4+x^4\right)-x^3+\left(2x^2-2x^2\right)-\left(x-4x\right)+\left(5-1\right)\)

\(=10x^4-x^3+3x+4\)

\(P\left(x\right)-Q\left(x\right)\)

\(=\left(9x^4+2x^2-x+5\right)-\left(x^4-x^3-2x^2+4x-1\right)\)

\(=9x^4+2x^2-x+5-x^4+x^3+2x^2-4x+1\)

\(=\left(9x^4-x^4\right)+x^3+\left(2x^2+2x^2\right)-\left(x+4x\right)+\left(5-1\right)\)

\(=8x^4+x^3+4x^2-5x+4\)

Giúp tớ đi các cậu ơi, mai phải nộp rồi

A(x) = x² + 5x⁴ - 3x³ + x² - 4x⁴ + 3x³ - x + 5

       = ( 5x⁴ - 4x⁴ ) + ( 3x³ - 3x³ ) + ( x² + x² ) - x + 5

       = x⁴ + 2x² - x + 5

B(x) = x - 5x³ - x² - x⁴ + 5x³ - x² - 3x + 1

        = -x⁴ + ( 5x³ - 5x³ ) + ( -x² - x² ) + ( -3x + x ) + 1

        = -x⁴ - 2x² - 2x + 1

M(x) = A(x) + B(x) 

         = x⁴ + 2x² - x + 5 + ( -x⁴ - 2x² - 2x + 1 )

         =  x⁴ + 2x² - x + 5 - x⁴ - 2x² - 2x + 1

         = -3x + 6

N(x) = A(x) - B(x) 

        = x⁴ + 2x² - x + 5 - ( -x⁴ - 2x² - 2x + 1 )

        = x⁴ + 2x² - x + 5 + x⁴ + 2x² + 2x - 1

        = 2x⁴ + 4x² + x + 4

M(x) = 0 <=> -3x + 6 = 0

              <=> -3x = -6

              <=> x = 2

Vậy nghiệm của M(x) là 2

a, Ta có : 

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

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

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

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

b, Ta có : \(M\left(x\right)=A\left(x\right)+B\left(x\right)=\left(x^4+2x^2-x+5\right)+\left(-x^4-2x^2-2x+1\right)\)

\(=-3x+6\)

Tương tự vs N(x) 

c, Đặt \(-3x+6=0\Leftrightarrow-3x=-6\Leftrightarrow x=2\)

1: Sửa đề: 3x-5

\(=\dfrac{-x^2\left(3x-5\right)-3\left(3x-5\right)}{3x-5}=-x^2-3\)

2: \(=\dfrac{5x^4-5x^3+14x^3-14x^2+12x^2-12x+8x-8}{x-1}\)

=5x^2+14x^2+12x+8

3: \(=\dfrac{5x^3+10x^2+4x^2+8x+4x+8}{x+2}=5x^2+4x+4\)

4: \(=\dfrac{\left(x^2-1\right)\left(x^2+1\right)-2x\left(x^2-1\right)}{x^2-1}=x^2+1-2x\)

5: \(=\dfrac{x^2\left(5-3x\right)+3\left(5-3x\right)}{5-3x}=x^2+3\)

Tách ra, dài quá mn đọc là mất hứng làm đó.