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polynomial

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P(x) = 2x^4 - x^3 + 2x^2 - k where k is an unknown integer. P(x) divided by (x+1) has a remainder of 2. What is the value of k?

Jul 10, 2020

#1
+10610
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P(x) = 2x^4 - x^3 + 2x^2 - k where k is an unknown integer. P(x) divided by (x+1) has a remainder of 2. What is the value of k?

Hello Guest!

P (x) = 2x ^ 4 - x ^ 3 + 2x ^ 2 - k wobei k eine unbekannte ganze Zahl ist. P (x) geteilt durch (x + 1) hat einen Rest von 2. Was ist der Wert von k?

$$P_v(x) =\frac{ 2x^4 - x^3 + 2x^2 - k }{x+1}$$

$$2x^4 - x^3 + 2x^2 - k :{\color{blue}(x+1)}=$$$$2x^3-3x^2+4x-\frac{k}{x}-\ ...$$

$$\underline{2x^4+2x^3}$$

$$-3x^3-2x^2$$

$$\underline{-3x^3-3x^2}$$

$$5x^2-k$$

$$\underline{5x^2+4x}$$

$$-k-4x$$

$$\large\frac{{\color{blue}2}-k-4x}{x+1}=\color{blue}\mathbb Z$$