Question

Using remainder theorem ,find the remainder when p (x) is divided by q (x) where p (x)=x³-3x²+4x-5, q(x)=(x-a).​

Answer 1

Answer:

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Answer 2

$\underline{ \pink{ Remainder \: Theorem: }}$

If p(x) is any polynomial of degree greater than or equal to 1 and p(x) is divided by the linear polynomial (x-a) , then the remainder is p(a).

$Given \: p(x) = x^{3}-3x^{2}+4x-5, \\and \:q(x) = (x-a)$

$If \: p(x) \:is \: divided \:by \:q(x)\:then \: the \\remainder \: is \: p(a)$

$\red{ Required \: remainder } \\= p(a) \\= a^{3}-3\times a^{2} + 4\times a - 5 \\= a^{3}-3 a^{2} + 4a - 5$

Therefore.,

$\red{ Required \: remainder }$

$\green { = a^{3}-3 a^{2} + 4a - 5}$

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