Vũ Trần Minh Anh
Giới thiệu về bản thân
2x4 | \(- 3 x^{3}\) | \(- 3 x^{2}\) | \(+ 6 x\) | \(- 2\)
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\(x^{2} - 2\) | |
\(2 x^{4}\) |
| \(- 4 x^{2}\) |
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\(2 x^{2} - 3 x + 1\) | |
| \(-\) | \(- 3 x^{3}\) | \(+ x^{2}\) | \(+ 6 x\) | \(- 2\) |
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| \(- 3 x^{3}\) |
| \(+ 6 x\) |
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| |
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| \(-\) | \(x^{2}\) |
| \(- 2\) |
|
|
| \(x^{2}\) |
| \(- 2\) |
| |
|
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|
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| \(0\) |
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Vậy ta có phép chia hết và thương là \(Q = 2 x^{2} - 3 x + 1\).
a) \(P \left(\right. x \left.\right) + Q \left(\right. x \left.\right)\)
\(= \left(\right. x^{4} - 5 x^{3} + 4 x - 5 \left.\right) + \left(\right. - x^{4} + 3 x^{2} + 2 x + 1 \left.\right)\)
\(= x^{4} - 5 x^{3} + 4 x - 5 - x^{4} + 3 x^{2} + 2 x + 1\)
\(= \left(\right. x^{4} - x^{4} \left.\right) - 5 x^{3} + 3 x^{2} + \left(\right. 4 x + 2 x \left.\right) + \left(\right. 1 - 5 \left.\right)\)
\(= - 5 x^{3} + 3 x^{2} + 6 x - 4\)
b) \(R \left(\right. x \left.\right) = P \left(\right. x \left.\right) - Q \left(\right. x \left.\right)\)
\(= \left(\right. x^{4} - 5 x^{3} + 4 x - 5 \left.\right) - \left(\right. - x^{4} + 3 x^{2} + 2 x + 1 \left.\right)\)
\(= x^{4} - 5 x^{3} + 4 x - 5 + x^{4} - 3 x^{2} - 2 x - 1\)
\(= \left(\right. x^{4} + x^{4} \left.\right) - 5 x^{3} - 3 x^{2} + \left(\right. 4 x - 2 x \left.\right) + \left(\right. - 1 - 5 \left.\right)\)
\(= 2 x^{4} - 5 x^{3} - 3 x^{2} + 2 x - 6\)
a) \(P \left(\right. x \left.\right) + Q \left(\right. x \left.\right)\)
\(= \left(\right. x^{4} - 5 x^{3} + 4 x - 5 \left.\right) + \left(\right. - x^{4} + 3 x^{2} + 2 x + 1 \left.\right)\)
\(= x^{4} - 5 x^{3} + 4 x - 5 - x^{4} + 3 x^{2} + 2 x + 1\)
\(= \left(\right. x^{4} - x^{4} \left.\right) - 5 x^{3} + 3 x^{2} + \left(\right. 4 x + 2 x \left.\right) + \left(\right. 1 - 5 \left.\right)\)
\(= - 5 x^{3} + 3 x^{2} + 6 x - 4\)
b) \(R \left(\right. x \left.\right) = P \left(\right. x \left.\right) - Q \left(\right. x \left.\right)\)
\(= \left(\right. x^{4} - 5 x^{3} + 4 x - 5 \left.\right) - \left(\right. - x^{4} + 3 x^{2} + 2 x + 1 \left.\right)\)
\(= x^{4} - 5 x^{3} + 4 x - 5 + x^{4} - 3 x^{2} - 2 x - 1\)
\(= \left(\right. x^{4} + x^{4} \left.\right) - 5 x^{3} - 3 x^{2} + \left(\right. 4 x - 2 x \left.\right) + \left(\right. - 1 - 5 \left.\right)\)
\(= 2 x^{4} - 5 x^{3} - 3 x^{2} + 2 x - 6\)
a) \(P \left(\right. x \left.\right) + Q \left(\right. x \left.\right)\)
\(= \left(\right. x^{4} - 5 x^{3} + 4 x - 5 \left.\right) + \left(\right. - x^{4} + 3 x^{2} + 2 x + 1 \left.\right)\)
\(= x^{4} - 5 x^{3} + 4 x - 5 - x^{4} + 3 x^{2} + 2 x + 1\)
\(= \left(\right. x^{4} - x^{4} \left.\right) - 5 x^{3} + 3 x^{2} + \left(\right. 4 x + 2 x \left.\right) + \left(\right. 1 - 5 \left.\right)\)
\(= - 5 x^{3} + 3 x^{2} + 6 x - 4\)
b) \(R \left(\right. x \left.\right) = P \left(\right. x \left.\right) - Q \left(\right. x \left.\right)\)
\(= \left(\right. x^{4} - 5 x^{3} + 4 x - 5 \left.\right) - \left(\right. - x^{4} + 3 x^{2} + 2 x + 1 \left.\right)\)
\(= x^{4} - 5 x^{3} + 4 x - 5 + x^{4} - 3 x^{2} - 2 x - 1\)
\(= \left(\right. x^{4} + x^{4} \left.\right) - 5 x^{3} - 3 x^{2} + \left(\right. 4 x - 2 x \left.\right) + \left(\right. - 1 - 5 \left.\right)\)
\(= 2 x^{4} - 5 x^{3} - 3 x^{2} + 2 x - 6\)