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<blockquote data-quote="imhotep" data-source="post: 30125161" data-attributes="member: 562115"><p>ශේෂ ප්රමේය නැවත නැවත පාවිච්චි කරන්නෙ... This is exactly I asked before <strong>what's meant </strong>by this. I am not aware of such a thing. Sorry.</p><p></p><p>To find the remainder there a only a few ways, standard long division, then synthetic division and finally the remainder theorem. (there are others like using the Taylor series which can generalize the remainder when divided by (x-a)^m, but they are beyond the scope of A/L)</p><p></p><p>The remainder theorem states....</p><p></p><p>Let P(x) be a polynomial of degree n. If P(x) is divided by x-a , where 'a' is a real number then the remainder is P(a)</p><p>Note that the divisor has be <strong>linear.</strong></p><p></p><p>The remainder theorem <strong>can be extended</strong> <strong>to quadratic</strong> divisors</p><p></p><p>Let P(x) be a polynomial of degree n. If P(x) is divided by (x-a)(x-b), where both a & b are real, the remainder is of the form</p><p>R(x) = r1 x + r0 where both r0 & r1 are constants and found by solving </p><p>P(a) = r1 a + r2 & P(b) = r1 b + r2</p><p></p><p>Note - This doesn't work when the divisors are the same... (x-a)(x-a) or (x-a)^2</p><p></p><p>Hence AFAIK the derivative has to be used to solve for r0 and r1.</p><p></p><p>PS: If anyone knows about "ශේෂ ප්රමේය නැවත නැවත පාවිච්චි කරන්නෙ" please let us know. [USER=400100]@pdn.ac.lk[/USER] any ideas?</p></blockquote><p></p>
[QUOTE="imhotep, post: 30125161, member: 562115"] ශේෂ ප්රමේය නැවත නැවත පාවිච්චි කරන්නෙ... This is exactly I asked before [B]what's meant [/B]by this. I am not aware of such a thing. Sorry. To find the remainder there a only a few ways, standard long division, then synthetic division and finally the remainder theorem. (there are others like using the Taylor series which can generalize the remainder when divided by (x-a)^m, but they are beyond the scope of A/L) The remainder theorem states.... Let P(x) be a polynomial of degree n. If P(x) is divided by x-a , where 'a' is a real number then the remainder is P(a) Note that the divisor has be [B]linear.[/B] The remainder theorem [B]can be extended[/B] [B]to quadratic[/B] divisors Let P(x) be a polynomial of degree n. If P(x) is divided by (x-a)(x-b), where both a & b are real, the remainder is of the form R(x) = r1 x + r0 where both r0 & r1 are constants and found by solving P(a) = r1 a + r2 & P(b) = r1 b + r2 Note - This doesn't work when the divisors are the same... (x-a)(x-a) or (x-a)^2 Hence AFAIK the derivative has to be used to solve for r0 and r1. PS: If anyone knows about "ශේෂ ප්රමේය නැවත නැවත පාවිච්චි කරන්නෙ" please let us know. [USER=400100]@pdn.ac.lk[/USER] any ideas? [/QUOTE]
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