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Diketahui P dan Q suatu polinomial. Jika P(x) bert...

Diketahui P dan Q suatu polinomial. Jika P(x) berturut-turut memberikan sisa -1 dan 5 apabila dibagi x - 1 dan dibagi x + 2 , dan Q(x) berturut-turut memberikan sisa 1 dan -2 apabila dibagi x + 2 dan dibagi x - 1. maka P(Q(x)) dibagi begin mathsize 14px style straight x squared plus straight x minus 2 end style bersisa ....

  1. 2x - 3

  2. 2x + 3

  3. 3x + 2

  4. -3x + 2

  5. 3x - 2

Jawaban:

begin mathsize 14px style straight P left parenthesis straight x right parenthesis space dibagi space left parenthesis straight x minus 1 right parenthesis space sisanya space – 1 space maka space straight P left parenthesis 1 right parenthesis equals negative 1  straight P left parenthesis straight x right parenthesis space dibagi space left parenthesis straight x plus 2 right parenthesis space sisanya space 5 space maka space straight P left parenthesis negative 2 right parenthesis equals 5  straight Q left parenthesis straight x right parenthesis space dibagi space left parenthesis straight x minus 1 right parenthesis space sisanya space – 2 space space maka space straight Q left parenthesis 1 right parenthesis equals negative 2  straight Q left parenthesis straight x right parenthesis space dibagi space left parenthesis straight x plus 2 right parenthesis space sisanya space 1 space maka space straight Q left parenthesis negative 2 right parenthesis equals 1    straight x squared plus straight x minus 2 space difaktorkan space menjadi space left parenthesis straight x minus 1 right parenthesis left parenthesis straight x plus 2 right parenthesis    straight P left parenthesis straight Q left parenthesis straight x right parenthesis right parenthesis space dibagi space left parenthesis straight x minus 1 right parenthesis left parenthesis straight x plus 2 right parenthesis space sisanya space ax plus straight b  maka colon  straight P open parentheses straight Q open parentheses 1 close parentheses close parentheses equals straight a open parentheses 1 close parentheses plus straight b  straight P open parentheses negative 2 close parentheses equals straight a plus straight b  5 equals straight a plus straight b  straight b equals 5 minus straight a space left parenthesis persamaan space 1 right parenthesis  dan  straight P open parentheses straight Q open parentheses negative 2 close parentheses close parentheses equals straight a open parentheses negative 2 close parentheses plus straight b  straight P open parentheses 1 close parentheses equals negative 2 straight a plus straight b  minus 1 equals negative 2 straight a plus straight b space left parenthesis persamaan space 2 right parenthesis    Substitusi space persamaan space 1 space ke space persamaan space 2 colon  minus 1 equals negative 2 straight a plus 5 minus straight a  3 straight a equals 6  straight a equals 2    straight b equals 5 minus 2 equals 3    straight S equals ax plus straight b equals 2 straight x plus 3 end style

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