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# When the polynomial P(x) is divided by x − 2, the remainder is 7. Which of the following must be true?

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A:P(7)=2

B:P(2)=7

C:P(2)=0

D:P(-2)=7

Mar 13, 2018

#1
+1

When the polynomial P(x) is divided by x − 2, the remainder is 7.

Which of the following must be true?

P(2) = 7

Example:

$$\begin{array}{|rcll|} \hline x^3 - x^2 + 2x - 1 : x- 2 &=& x^2 + x + 4 + \dfrac{7}{x - 2} \\\\ P(2) = 7 \\\\ P(2) = 2^3 - 2^2 + 2\cdot 2 - 1 &=& 7 \\ 8-4+4 - 1 &=& 7 \\ \mathbf{ 7 } & \mathbf{=} & \mathbf{7} \\ \hline \end{array}$$ Mar 13, 2018
edited by heureka  Mar 13, 2018

#1
+1

When the polynomial P(x) is divided by x − 2, the remainder is 7.

Which of the following must be true?

P(2) = 7

Example:

$$\begin{array}{|rcll|} \hline x^3 - x^2 + 2x - 1 : x- 2 &=& x^2 + x + 4 + \dfrac{7}{x - 2} \\\\ P(2) = 7 \\\\ P(2) = 2^3 - 2^2 + 2\cdot 2 - 1 &=& 7 \\ 8-4+4 - 1 &=& 7 \\ \mathbf{ 7 } & \mathbf{=} & \mathbf{7} \\ \hline \end{array}$$ heureka Mar 13, 2018
edited by heureka  Mar 13, 2018