a: \(P\left(x\right)+Q\left(x\right)=9x^3-6x^2+x-3\)

\(P\left(x\right)-Q\left(x\right)=-x^3-6x^2+13x-7\)

b: \(P\left(1\right)=4-6+7-5=-2+7-5=0\)

\(P\left(-2\right)=-32-24-14-5=-73\)

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

\(P\left(x\right)-Q\left(x\right)=10x^3-7x^2+8x-14\)

b: \(P\left(1\right)=4-7+3-5=-5\)

\(P\left(-1\right)=-4-7-3-5=-19\)

a) \(P_{\left(x\right)}=2x^3-2x+x^2+3x+2\)

\(P_{\left(x\right)}=2x^3+x^2+x+2\)

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

\(Q_{\left(x\right)}=x^3+x^2+x+1\)

b) \(P_{\left(x\right)}+Q_{\left(x\right)}=\left(2x^3+x^2+x+2\right)+\left(x^3+x^2++x+1\right)\)

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

pls giúp mink với :(

` P(x) = x^3-2x^2+x-2`

`Q(x) = 2x^3 - 4x^2+ 3x – 5​​​​6`

a) `P(x) -Q(x)`

`= x^3-2x^2+x-2 - 2x^3 +4x^2 -3x +56`

`=(x^3-2x^3) +(4x^2-2x^2) +(x-3x) +(-2+56)`

`= -x^2 +2x^2 -2x +54`

b) Thay `x=2` vào `P(x)` ta đc

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

`= 8-8+2-2 =0`

Vậy chứng tỏ `x=2` là nghiệm của đa thức `P(x)`

Thay `x=2` vào `Q(x)` ta đc

`Q(2) = 2*2^3 -4*2^2 +3*2-56`

`=16 -16+6-56`

`= -50`

Vậy chứng tỏ `x=2` là ko nghiệm của đa thức `Q(x)`

P(x) + Q(x)= ( x^5 - 2x^2 + 7x^4 - 9x^3 - 1/4x) + ( 5x^4 - x^5 + 4x^2 - 2x^3 - 1/4)

                 = x^5 - 2x^2 + 7x^4 - 9x^3 - 1/4x + 5x^4 - x^5 + 4x^2 - 2x^3 - 1/4

                 = ( x^5 - x^5 ) - ( 2x^2 + 4x^2) + ( 7x^4 + 5x^4) - ( 9x^3 - 2x^3) - 1/4x - 1/4

                 =                            6x^2 + 12x^4 - 6x^3 - 1/4x - 1/4

P(x) - Q(x)=  ( x^5 - 2x^2 + 7x^4 - 9x^3 -1/4x) - ( 5x^4 - x^5 + 4x^2 - 2x^3 -1/4)

                 = x^5 - 2x^2 + 7x^4 - 9x^3 - 1/4x - 5x^4 + x^5 - 4x^2 + 2x^3 + 1/4

                 = ( x^5 + x^5) - ( 2x^2 - 4x^2) + ( 7x^4 - 5x^4) - ( 9x^3 + 2x^3) - 1/4x + 1/4

                 = 2x^5 - (-2)x^2 + 2x^4 - 11x^3 - 1/4x + 1/4

P(x)=x^5+  7x^4- 9x^3+ 2x^2-1/4x-0

Q(x)=(-x^5+5x^4- 2x^3+ 4x^2+0x-1/4

      =      12x^4-11x^3+ 6x^2-1/4x-1/4

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

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

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

b) \(P\left(x\right)+Q\left(x\right)=2x^3+3\); \(P\left(x\right)-Q\left(x\right)=2x^2+2x+1\)

a) Sắp xếp theo lũy thừa giảm dần

P(x)=x^5−3x^2+7x^4−9x^3+x^2−1/4x

=x^5+7x^4−9x^3−3x^2+x^2−1/4x

=x^5+7x^4−9x^3−2x^2−1/4x

Q(x)=5x^4−x^5+x^2−2x^3+3x^2−1/4

=−x^5+5x^4−2x^3+x^2+3x^2−1/4

=−x^5+5x^4−2x^3+4x^2−1/4

b)

P(x)+Q(x)

=(x^5+7x^4−9x^3−2x^2−1/4^x)+(−x^5+5x^4−2x^3+4x^2−1/4)

=x^5+7x^4−9x^3−2x^2−1/4x−x^5+5x^4−2x^3+4x^2−1/4

=(x^5−x^5)+(7x^4+5x^4)+(−9x^3−2x^3)+(−2x^2+4x^2)−1/4x−1/4

=12x^4−11x^3+2x^2−1/4x−1/4

P(x)−Q(x)

=(x^5+7x^4−9x^3−2x^2−1/4x)−(−x^5+5x^4−2x^3+4x^2−1/4)

=x^5+7x^4−9x^3−2x^2−1/4x+x^5−5x^4+2x^3−4x^2+1/4

=(x^5+x^5)+(7x^4−5x^4)+(−9x^3+2x^3)+(−2x^2−4x^2)−1/4x+1/4

=2x5+2x4−7x3−6x2−1/4x−1/4

c) Ta có

P(0)=0^5+7.0^4−9.0^3−2.0^2−1/4.0

⇒x=0là nghiệm của P(x).

Q(0)=−0^5+5.0^4−2.0^3+4.0^2−1/4=−1/4≠0

⇒x=0không phải là nghiệm của Q(x).

1: P(x)=M(x)+N(x)

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

=2x^2-8

2: P(x)=0

=>x^2-4=0

=>x=2 hoặc x=-2

3: Q(x)=M(x)-N(x)

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

=-4x^3+8x+2

P(x) + Q(x) = 4x³ + x² - x + 5 + ( -2 )x² + 4x - 1

                   = 4x³ + ( 1 - 2 )x² + ( 4 - 1 )x + ( 5 - 1 )

                   = 4x³ - x² + 3x + 4

P(x) - Q(x) = ( 4x³ + x² - x + 5 ) - ( -2x² + 4x - 1 )

                  = 4x³ + x² - x + 5 + 2x² - 4x + 1

                  = 4x³ + ( 1 + 2 )x² -x - 4x + ( 5 + 1 )

                  = 4x³ + 3x² - 5x + 6