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`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`
\(a,P\left(x\right)=2x^3-x+x^2-x^3+3x+5\\ =\left(2x^3-x^3\right)+x^2+\left(-x+3x\right)+5\\ =x^3+x^2+2x+5\\ Q\left(x\right)=3x^3+4x^2+3x-4x^3-5x^2+10\\ =\left(3x^3-4x^3\right)+\left(4x^2-5x^2\right)+3x+10\\ =-x^3-x^2+3x+10\\ b,M\left(x\right)=P\left(x\right)+Q\left(x\right)=x^3+x^2+2x+5-x^3-x^2+3x+10\\ =\left(x^3-x^3\right)+\left(x^2-x^2\right)+\left(2x+3x\right)+\left(5+10\right)=5x+15\\ N\left(x\right)=P\left(x\right)-Q\left(x\right)=x^3+x^2+2x+5-\left(-x^3-x^2+3x+10\right)\\ =x^3+x^2+2x+5+x^3+x^2-3x-10\\ =\left(x^3+x^3\right)+\left(x^2+x^2\right)+\left(2x-3x\right)+\left(5-10\right)\\ =2x^3+2x^2-x-5\)
`a,P(x)= 2x^3 -x+x^2 -x^3 +3x+5`
`= (2x^3 -x^3)+x^2+(-x+3x) +5`
`= x^3 +x^2 + 2x+5`
`Q(x)=3x^3 +4x^2+3x-4x^3-5x^2+10`
`= (3x^3-4x^3)+(4x^2-5x^2)+3x+10`
`= -x^3 -x^2+3x+10`
`b,M(x)=P(x)+Q(x)`
`->M(x)=(x^3 +x^2 + 2x+5)+(-x^3 -x^2+3x+10)`
`=x^3 +x^2 + 2x+5+(-x^3) -x^2+3x+10`
`=(x^3 -x^3)+(x^2 -x^2)+(2x+3x)+(5+10)`
`= 5x+15`
`N(x)=P(x)-Q(x)`
`->N(x)=(x^3 +x^2 + 2x+5)-(-x^3 -x^2+3x+10)`
`=x^3 +x^2 + 2x+5-x^3 +x^2-3x-10`
`=(x^3-x^3)+(x^2+x^2)+(2x-3x)+(5-10)`
`=2x^2 -x-5`
\(a,Q_{\left(x\right)}=-4x^3+2x-2+2x-x^2-1\\ Q_{\left(x\right)}=-4x^3-x^2+4x-3\\ P_{\left(x\right)}=4x^3-3x+x^2+7+x\\ P_{\left(x\right)}=4x^3+x^2-2x+7\)
\(b,M_{\left(x\right)}=P_{\left(x\right)}+Q_{\left(x\right)}\\ M_{\left(x\right)}=4x^3+x^2-2x+7-4x^3-x^2+4x-3\\ M_{\left(x\right)}=2x+4\)
\(N_{\left(x\right)}=4x^3+x^2-2x+7+4x^2+x^2-4x+3\\ N_{\left(x\right)}=8x^3+2x^2-6x+10\)
\(c,M_{\left(x\right)}=0\\ \Rightarrow2x+4=0\\ \Rightarrow2x=-4\\ \Rightarrow x=-2\)
a: \(P\left(x\right)=4x^3+x^2-2x+7\)
\(Q\left(x\right)=-4x^3-x^2+4x-3\)
b: \(M\left(x\right)=4x^3+x^2-2x+7-4x^3-x^2+4x-3=2x+4\)
\(N\left(x\right)=8x^3+2x^2-6x+10\)
c: Đặt M(x)=0
=>2x+4=0
hay x=-2
a) (5x3 – 2x2 + 4x – 4) . ( x3 + 3x2 – 5)
= 5x3 . ( x3 + 3x2 – 5) - 2x2 . ( x3 + 3x2 – 5) + 4x . ( x3 + 3x2 – 5) – 4 . ( x3 + 3x2 – 5)
= 5x3 . x3 + 5x3 . 3x2 + 5x3 . (-5) – [ 2x2 . x3 + 2x2 . 3x2 +2x2 . (-5)] + [4x . x3 + 4x. 3x2 + 4x . (-5)] – [ 4x3 + 4.3x2 + 4.(-5)]
= 5x6 + 15x5 – 25x3 – (2x5 + 6x4 – 10x2) + 4x4 + 12x3 – 20x – (4x3 + 12x2 – 20)
= 5x6 + 15x5 – 25x3 – 2x5 - 6x4 + 10x2 + 4x4 + 12x3 – 20x – 4x3 - 12x2 + 20
= 5x6 + (15x5 – 2x5 ) + (- 6x4 + 4x4 ) + (-25x3 + 12x3 – 4x3 ) + (10x2 - 12x2 ) – 20x + 20
= 5x6 + 13x5 – 2x4 – 17x3 -2x2 – 20x + 20
b) (-2,5.x4 + 0,5x2 + 1) . (4x3 – 2x + 6)
= -2,5.x4 . (4x3 – 2x + 6) + 0,5x2 . (4x3 – 2x + 6) + 1. (4x3 – 2x + 6)
= (-2,5.x4) . 4x3 + (-2,5.x4 ) . (-2x) + (-2,5.x4 ) . 6 + 0,5x2 . 4x3 + 0,5x2 . (-2x) + 0,5x2 . 6 + 4x3 – 2x + 6
= -10x7 + 5x5 – 15x4 + 2x5 – x3 + 3x2 + 4x3 – 2x + 6
= -10x7 + ( 5x5 + 2x5 ) - 15x4 + (– x3 + 4x3 ) + 3x2 – 2x + 6
= -10x7 +7x5 - 15x4 + 3x3 + 3x2 – 2x + 6
M-N-P=4x3-2x2y+xy+1-3x2y-2xy+5-4x3+5x2y-3xy-1
=-4xy+5
p-n-m=4x3-5x2y+3x2y+1-3x2y-2xy+5-4x3+2x2y-xy-1
=-6x2y+5
a: M(x)=5x^4+4x^3+2x+1-5x^4+x^3+3x^2+x-1
=5x^3+3x^2+3x
b: N(x)=5x^4+4x^3+2x+1+5x^4-x^3-3x^2-x+1
=10x^4+3x^3-3x^2+x+2
`@` `\text {dnammv}`
` \text {M(x)-A(x)=B(x)}`
`-> \text {M(x)=A(x)+B(x)}`
`-> M(x)=(5x^4 + 4x^3 + 2x + 1)+(-5x^4 + x^3 + 3x^2 + x - 1)`
`= 5x^4 + 4x^3 + 2x + 1-5x^4 + x^3 + 3x^2 + x - 1`
`= (5x^4-5x^4)+(4x^3+x^3)+3x^2+(2x+x)+(1-1)`
`= 5x^3+3x^2+3x`
`b,`
`\text {N(x)=A(x)-B(x)}`
`N(x)=(5x^4 + 4x^3 + 2x + 1)-(-5x^4 + x^3 + 3x^2 + x - 1)`
`= 5x^4 + 4x^3 + 2x + 1+5x^4 - x^3 - 3x^2 - x + 1`
`= (5x^4+5x^4)+(4x^3-x^3)-3x^2+(2x-x)+(1+1)`
`= 10x^4+3x^3-3x^2+x+2`
Ta đặt và thực hiện các phép tính N + M và N – M có
Vậy: N - M = - 9y5 + 11y3 + y – 1 ; N + M = 7y5 + 11y3 - 5y + 1.