Question

1.Cho hai đa thức: P(x)=5x³-\(\dfrac{1}{3}\)+7x⁴+8x²

và Q(x)=8x²-5x-3x³+x⁴-\(\dfrac{2}{3}\)

Hãy tính P(x)+Q(x)và P(x)-Q(x)

Answer 1

P(x)+Q(x)=(5x³-+7x⁴+8x²)+(8x²-5x-3x³+x⁴)

= 5x³-7x⁴+8x²+8x²-5x-3x³+x⁴

=(5x³-3x³)+(-7x⁴+x⁴)+(8x²+8x²)-5x

=2x³-6x⁴+16x²-5x

P(x)-Q(x)=(5x³-+7x⁴+8x²)-(8x²-5x-3x³+x⁴)

= 5x³-+7x⁴+8x²-8x²+5x+3x³-x⁴

=(5x³+3x³)+(-7x^4_x⁴)+(8x^2-8x²)+5x

= 8x³-8x⁴+5x

Answer 2

*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 - \(\dfrac{1}{3}\)

Answer 3

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

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

*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

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

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

Answer 4

*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

Answer 5

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