a: P(x)=5x^3+3x^2-2x-5

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

b: P(x)-Q(x)=x^2-9

P(x)+Q(x)=10x^3+5x^2-4x-1

c: P(x)-Q(x)=0

=>x^2-9=0

=>x=3; x=-3

d: C=A*B=-7/2x^6y^4

a: P(x)=6x^4+5x^3-3x^2+5x-10

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

b: P(x)+Q(x)

=6x^4+5x^3-3x^2+5x-10+5x^4+5x^3+2x^2-4x+4

=11x^4+10x^3-x^2+x-6

P(x)-Q(x)

=6x^4+5x^3-3x^2+5x-10-5x^4-5x^3-2x^2+4x-4

=x^4-5x^2+9x-14

a: P(x)=6x^4+5x^3-3x^2+5x-10

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

b: P(x)+Q(x)

=6x^4+5x^3-3x^2+5x-10+5x^4+5x^3+2x^2-4x+4

=11x^4+10x^3-x^2+x-6

P(x)-Q(x) =6x^4+5x^3-3x^2+5x-10-5x^4-5x^3-2x^2+4x-4

=x^4-5x^2+9x-14

a)P(x) = 7x³ - x² + 5x - 2x³ +6 - 8x

=5x^3-x^2-3x+6

 Q(x) = -2x + x³ - 4x² + 3 - 5x²

=x^3-9x^2-2x+3

b)

P(x) - Q(x)=4^3+8x^2-x-3

P(x) + Q(x)=6^3-10x^2-5x+9

a: \(P\left(x\right)=-5x^4+2x^2-8x+\dfrac{1}{2}\)

\(Q\left(x\right)=4x^4+2x^3-5x^2-6x+\dfrac{3}{2}\)

b: \(A\left(x\right)=-5x^4+2x^2-8x+\dfrac{1}{2}+4x^4+2x^3-5x^2-6x+\dfrac{3}{2}=-x^4+2x^3-3x^2-14x+2\)

\(B\left(x\right)=-5x^4+2x^2-8x+\dfrac{1}{2}-4x^4-2x^3+5x^2+6x-\dfrac{3}{2}=-9x^4-2x^3+7x^2-2x-1\)

a)\(Q\left(x\right)=2x^3+4x^4-6x-5x^2+\dfrac{3}{2}\)

\(P\left(x\right)=2x^2-5x^4-8x+\dfrac{1}{2}\)

\(A\left(x\right)=2x^3-x^4-3x^2+2-14x\)

\(B\left(x\right)=-2x^3-9x^4-2x+7x^2-1\)

a: P(x)=-5x^3+6x^2+3x-1

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

b: H(x)=-5x^3+6x^2+3x-1-5x^3+6x^2+4x+2

=-10x^3+12x^2+7x+1

T(x)=-5x^3+6x^2+3x-1+5x^3-6x^2-4x-2

=-x-3

c: T(x)=0

=>-x-3=0

=>x=-3

d: G(x)=-(-10x^3+12x^2+7x+1)

=10x^3-12x^2-7x-1

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

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

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

c: Bậc của H(x) là 3

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

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

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

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

c) Bậc : 3

d)\(H\left(3\right)=-4.3^3+2.3^2+4.3=-4.27+2.9+12=-108+18+12=-78\)

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

\(H\left(-3\right)=-4.\left(-27\right)+2.9-12=108+18-12=114\)

\(H\left(\dfrac{1}{3}\right)=-4.\left(\dfrac{1}{3}\right)^3+2.\left(\dfrac{1}{3}\right)^2+\dfrac{4.1}{3}=-\dfrac{4.1}{27}+\dfrac{2.1}{9}+\dfrac{4}{3}\)

\(H\left(\dfrac{1}{3}\right)=-\dfrac{4}{27}+\dfrac{6}{27}+\dfrac{36}{27}=\dfrac{38}{27}\)

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).