13. B

14. D

15. D

16. A

17. B

18. D

19. C

20. C

b) R(x) = f(x) - h(x)

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

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

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

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

Vậy R(x) = 5x\(^3\) - 1x\(^2\) - 4x - 1

a) P(x) = f(x) - g(x)

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

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

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

= 3x\(^3\) - 2x\(^2\) - 8x - 3

Vậy P(x) = 3x\(^3\) - 2x\(^2\) - 8x - 3

*Cách 1: Hàng ngang:

P(x) - Q(x) = (5x\(^3\) - \(\dfrac{1}{3}\) + 7x\(^4\) + 8x\(^2\)) - (8x\(^2\) - 5x - 3x\(^3\) + x\(^4\) - \(\dfrac{2}{3}\))

= 5x\(^3\) - \(\dfrac{1}{3}\) + 7x\(^4\) + 8x\(^2\) - 8x\(^2\) + 5x + 3x\(^3\) - x\(^4\) +\(\dfrac{2}{3}\)

= (5x\(^3\) + 3x\(^3\)) + (-\(\dfrac{1}{3}\) + \(\dfrac{2}{3}\)) + (7x\(^4\) - x\(^4\)) + (8x\(^2\) - 8x\(^2\)) + 5x

= 8x\(^3\) + \(\dfrac{1}{3}\) + 6x\(^4\) + 5x

Vậy P(x) - Q(x) = 8x\(^3\) + \(\dfrac{1}{3}\) + 6x\(^4\) + 5x

*Cách 2: Hàng dọc:

P(x) = 7x\(^4\) + 5x\(^3\) + 8x\(^2\) + 0x - \(\dfrac{1}{3}\)

-

Q(x) = x\(^4\) - 3x\(^3\) + 8x\(^2\) - 5x - \(\dfrac{2}{3}\)

Hay: P(x) = 7x\(^4\) + 5x\(^3\) + 8x\(^2\) + 0x - \(\dfrac{1}{3}\)

+

[-Q(x)] = -x\(^4\) + 3x\(^3\) - 8x\(^2\) + 5x + \(\dfrac{2}{3}\)

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P(x) - Q(x) = 6x\(^4\) + 8x\(^3\) + 5x - \(\dfrac{1}{3}\)

Vậy P(x) - Q(x) = 6x\(^4\) + 8x\(^3\) + 5x - \(\dfrac{1}{3}\)

*Cách 2: Hàng dọc:

P(x) = 7x\(^4\) + 5x\(^3\) + 8x\(^2\) + 0x - \(\dfrac{1}{3}\)

+

Q(x) = x\(^4\) - 3x\(^3\) + 8x\(^2\) - 5x - \(\dfrac{2}{3}\)

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P(x) + Q(x) = 8x\(^4\) - 2x\(^3\) + 16x\(^2\) - 5x - 1