a: \(A\left(x\right)=2x^4-x^3+3x^2+9x-2\)

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

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

A(x): bậc 4; hệ số cao nhất là 2; hệ số tự do là -2

B(x): bậc 4; hệ số cao nhất là 4; hệ số tự do là 9

b: M(x)=A(x)+B(x)=4x^4-6x^3+3x^2+8x+7

N(x)=B(x)-A(x)=-4x^3-3x^2-10x+11

c: Q(x)=-N(x)=4x^3+3x^2+10x-11

Ta có: A(x) = -4x⁵ - x³ + 4x² + 5x + 9 + 4x⁵ - 6x² - 2

A(x) = (-4x⁵ + 4x⁵) - x³ + (4x² - 6x²) + 5x + (9 - 2)

A(x) = -x³ - 2x² + 5x + 7

B(x) = -3x⁴ - 2x³ + 10x² - 8x + 5x³ - 7 - 2x³ + 8x

B(x) = -3x⁴ - (2x³ - 5x³ + 2x³) + 10x² - (8x - 8x) - 7

B(x) = -3x⁴ + x³ + 10x² - 7

A(x) + B(x) = (-x³ - 2x² + 5x + 7) + (-3x⁴ + x³ + 10x² - 7)

  = -x³ - 2x² + 5x + 7 - 3x⁴ + x³ + 10x² - 7

 = (-x³ + x³) - (2x² - 10x²) + 5x + (7 - 7)

 = 8x² + 5x

A(x) - B(x) = (-x^3 - 2x^2 + 5x + 7) - (-3x^4 + x^3 + 10x^2 - 7)

= -x^3 - 2x^2 + 5x + 7 + 3x^4 - x^3 - 10x^2 + 7

= (-x^3 - x^3) - (2x^2 + 10x^2) + 5x + (7 + 7)

= -2x^3 - 12x^2 + 5x + 14

\(A\left(x\right)=-x^3-2x^2+5x+7\)

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

\(A\left(x\right)+B\left(x\right)=8x^2+5x\)

\(A\left(x\right)-B\left(x\right)=-2x^3-12x^2+5x+14\)

Bài 1 ( a )

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

\(=-x^3-2x^2+5x-7\)

\(B_x=-3x^4-2x^3+10x^2-8x+5x^3-7-2x^3+8x\)

\(=-3x^4+x^3+10x^2-7\)

Bài 1 ( b )

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

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

\(=3x^4-2x^2+15x-14\)

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

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

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

Bài 2 \(a,\)

\(F_x-G_x+H_x=\left(x^3-2x^2+3x+1\right)-\left(x^3+x-1\right)+\left(2x^2-1\right)\)

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

\(=2x+1\)

\(b,\)\(F_x-G_x+H_x=0\)

\(\Rightarrow2x+1=0\)

\(\Rightarrow2x=-1\)

\(\Leftrightarrow x=-\frac{1}{2}\)

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, A(x) = -4x⁵ - x³ + 4² + 5x + 7 + 4x⁵ - 6x²

= ( 4x⁵ - 4x⁵) - x³ + ( 4x² - 6x²) + 5x + 7

= -x³ - 2x² +5x +7

B(x) = -3x⁴ - 4x³ + 10x² - 8x + 5x³ -7 +8x

= -3x⁴ + ( 5x³ - 4x³ ) + 10x² + ( 8x - 8x )

= -3x⁴ + x³ + 10x²

b, A(x) = -x³ - 2x² + 5x +7

+

B(x) = -3x⁴ + x³ + 10x²

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P(x) = A(x) +B(x) = -3x⁴ + 8x² + 5x + 7

A(x) = -x³ - 2x² + 5x + 7

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B(x) = -3x⁴ + x³ + 10x²

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Q(x) = A(x) - B(x) = 3x⁴ - 2x³ - 12x² + 5x + 7

a) A(x) = 5x⁴ - 5 + 6x³ + x⁴ - 5x - 12

= (5x⁴ + x⁴) + (- 5 - 12) + 6x³ - 5x

= 6x⁴ - 17 + 6x³ - 5x

= 6x⁴ + 6x³ - 5x - 17

B(x) = 8x⁴ + 2x³ - 2x⁴ + 4x³ - 5x - 15 - 2x²

= (8x⁴ - 2x⁴) + (2x³ + 4x³) - 5x - 15 - 2x²

= 4x⁴ + 6x³ - 5x - 15 - 2x²

= 4x⁴ + 6x³ - 2x² - 5x - 15

b) C(x) = A(x) - B(x)

=  6x⁴ + 6x³ - 5x - 17 - (4x⁴ + 6x³ - 2x² - 5x - 15)

= 6x⁴ + 6x³ - 5x - 17 - 4x⁴ - 6x³ + 2x² + 5x + 15

= ( 6x⁴ - 4x⁴) + ( 6x³ - 6x³) + (- 5x + 5x) + (-17 + 15) + 2x²

= 2x⁴ - 2 + 2x² 

= 2x⁴ + 2x² - 2