a: \(P\left(x\right)=4x^3+x^2-2x+7\)

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

b: \(M\left(x\right)=4x^3+x^2-2x+7-4x^3-x^2+4x-3=2x+4\)

\(N\left(x\right)=8x^3+2x^2-6x+10\)

c: Đặt M(x)=0

=>2x+4=0

hay x=-2

\(a,Q_{\left(x\right)}=-4x^3+2x-2+2x-x^2-1\\ Q_{\left(x\right)}=-4x^3-x^2+4x-3\\ P_{\left(x\right)}=4x^3-3x+x^2+7+x\\ P_{\left(x\right)}=4x^3+x^2-2x+7\)

\(b,M_{\left(x\right)}=P_{\left(x\right)}+Q_{\left(x\right)}\\ M_{\left(x\right)}=4x^3+x^2-2x+7-4x^3-x^2+4x-3\\ M_{\left(x\right)}=2x+4\)

\(N_{\left(x\right)}=4x^3+x^2-2x+7+4x^2+x^2-4x+3\\ N_{\left(x\right)}=8x^3+2x^2-6x+10\)

\(c,M_{\left(x\right)}=0\\ \Rightarrow2x+4=0\\ \Rightarrow2x=-4\\ \Rightarrow x=-2\)

a)\(P\left(x\right)=4x^3+x^2-2x+7\)

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

b)\(M\left(x\right)=4x^3+x^2-2x+7-4x^3-x^2-4x+3\)

\(M\left(x\right)=-6x+10\)

\(N\left(x\right)=4x^3+x^2-2x+7+4x^3+x^2+4x-3\)

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

c) cho M(x) = 0

\(=>-6x+10=0\)

\(-6x=-10\Rightarrow x=-\dfrac{10}{-6}=\dfrac{5}{3}\)

Ta có

P ( x ) = 2 x 3 − 3 x + x 5 − 4 x 3 + 4 x − x 5 + x 2 − 2 = x 5 − x 5 + 2 x 3 − 4 x 3 + x 2 + ( 4 x − 3 x ) − 2 = − 2 x 3 + x 2 + x − 2  Và  Q ( x ) = x 3 − 2 x 2 + 3 x + 1 + 2 x 2 = x 3 + − 2 x 2 + 2 x 2 + 3 x + 1 = x 3 + 3 x + 1

Khi đó

M ( x ) = P ( x ) + Q ( x ) = − 2 x 3 + x 2 + x − 2 + x 3 + 3 x + 1 = − 2 x 3 + x 2 + x − 2 + x 3 + 3 x + 1 = − 2 x 3 + x 3 + x 2 + ( x + 3 x ) − 2 + 1 = − x 3 + x 2 + 4 x − 1

Bậc của  M ( x )   =   - x 3   +   x 2   +   4 x   -   1   l à   3

Chọn đáp án C

Ta có

P ( x ) = 2 x 3 − 3 x + x 5 − 4 x 3 + 4 x − x 5 + x 2 − 2 = x 5 − x 5 + 2 x 3 − 4 x 3 + x 2 + ( 4 x − 3 x ) − 2 = − 2 x 3 + x 2 + x − 2  Và  Q ( x ) = x 3 − 2 x 2 + 3 x + 1 + 2 x 2

= x 3 + - 2 x 2 + 2 x 2 + 3 x + 1 = x 3 + 3 x + 1

Khi đó

P ( x ) − Q ( x ) = − 2 x 3 + x 2 + x − 2 − x 3 + 3 x + 1 = − 2 x 3 + x 2 + x − 2 − x 3 − 3 x − 1 = − 2 x 3 − x 3 + x 2 + ( x − 3 x ) − 2 − 1 = − 3 x 3 + x 2 − 2 x − 3

Chọn đáp án B

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

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

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

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

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

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

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

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

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

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

dsssws

a: P(x)=x^3+x^2+x+2

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

b: M(x)=P(x)+Q(x)

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

=2x^2+3

N(x)=x^3+x^2+x+2+x^3-x^2+x-1

=2x^3+2x+1

c: M(x)=2x^2+3>=3>0 với mọi x

=>M(x) ko có nghiệm

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

 \(=2x^4+7x^3-2x^2+2x+6\)

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

\(=-2x^4-10x^3+6x^2-2x-4\)

b) \(P\left(x\right)+Q\left(x\right)=2x^4+7x^3-2x^2+2x+6-2x^4-10x^3+6x^2-2x-4\)

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

Mình xp giúp được mỗi câu đầu thôi nha ;-;;;; 2 câu sau mình chưa học, bạn thông cảm ;-;;;.

`a,` \(\text{P(x) =}\)\(2x^3-3x+x^5-4x^3+4x-x^5+x^2-2\)

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

`P(x)= -2x^3- (-x)+0+x^2-2`

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

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

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

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