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Byju's Answer

Standard IX

Mathematics

Remainder Theorem

If px = x42...

Question

If $p (x) = x^{42} - 2 k$ is divided by $(x + 1)$ the remainder is $9$ , what is the value of $k$ ?

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Solution

Given $p (x) = x^{42} - 2 k$
$q (x) = x + 1$
We have given the remainder $= 9$
$∴ p (- 1) = 9$
$∴ p (- 1) = (- 1)^{42} - 2 k = 9$
$\Rightarrow 1 - 2 k = 9$
$= 2 k = - 8$
$\Rightarrow k = - 4$ .

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If p(x)=x42−2k is divided by (x+1) the remainder is 9, what is the value of k?

Given p(x)=x42−2kq(x)=x+1We have given the remainder=9∴p(−1)=9∴p(−1)=(−1)42−2k=9⇒1−2k=9=2k=−8⇒k=−4.

If $p (x) = x^{42} - 2 k$ is divided by $(x + 1)$ the remainder is $9$ , what is the value of $k$ ?

Given $p (x) = x^{42} - 2 k$
$q (x) = x + 1$
We have given the remainder $= 9$
$∴ p (- 1) = 9$
$∴ p (- 1) = (- 1)^{42} - 2 k = 9$
$\Rightarrow 1 - 2 k = 9$
$= 2 k = - 8$
$\Rightarrow k = - 4$ .