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If-f-x-x-1-g-x-2-and-g-3-4-Find-the-remainder-if-f-x-divided-by-x-1-x-3-

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Question Number 19811 by Joel577 last updated on 16/Aug/17
If f(x) = (x +1)g(x) − 2 and g(3) = 4 Find the remainder if f(x) divided by (x + 1)(x − 3)
Iff(x)=(x+1)g(x)−2andg(3)=4Findtheremainderiff(x)dividedby(x+1)(x−3)
Commented by myintkhaing last updated on 16/Aug/17
Since, f(x) = (x+1)g(x) −2 and g(3) = 4 when f(x) is divided by (x+1), the remainder, f(−1) = −2 and f(3) = 4g(3) −2 = 14 Let the quotient be Q(x) and the remainder be ax+b when f(x) is divided by (x+1)(x−3) So, f(x) = (x+1)(x−3)Q(x)+ax+b thus f(−1) = −a+b = −2 .........(1) f(3) = 3a+b = 14 .........(2) Solving equations (1) and (2) a = 4 and b = 2 ∴ The required remainder = 4x+2 #
Since,f(x)=(x+1)g(x)−2andg(3)=4whenf(x)isdividedby(x+1),theremainder,f(−1)=−2andf(3)=4g(3)−2=14LetthequotientbeQ(x)andtheremainderbeax+bwhenf(x)isdividedby(x+1)(x−3)So,f(x)=(x+1)(x−3)Q(x)+ax+bthusf(−1)=−a+b=−2………(1)f(3)=3a+b=14………(2)Solvingequations(1)and(2)a=4andb=2You can't use 'macro parameter character #' in math mode
Commented by Joel577 last updated on 16/Aug/17
thank you very much
thankyouverymuch

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