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Jika sisa pembagian polinomial x4−4x2+6x2+ax+2 oleh x−3 adalah 14, nilai a adalah ...

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Jika sisa pembagian polinomial begin mathsize 14px style x to the power of 4 minus 4 x squared plus 6 x squared plus a x plus 2 end style oleh begin mathsize 14px style x minus 3 end style adalah 14, nilai begin mathsize 14px style a end style adalah ...

L. Marlina

Master Teacher

Mahasiswa/Alumni Institut Teknologi Bandung

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Jawaban

nilai begin mathsize 14px style a end style adalah begin mathsize 14px style negative 5 end style.

Pembahasan

misalkan begin mathsize 14px style f open parentheses x close parentheses equals x to the power of 4 minus 4 x squared plus 6 x squared plus a x plus 2 end style dibagi oleh begin mathsize 14px style x minus 3 end style, maka sisa pembagiannya adalah begin mathsize 14px style f open parentheses 3 close parentheses end style.

begin mathsize 14px style space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space f open parentheses 3 close parentheses equals 14 3 to the power of 4 minus 4 open parentheses 3 close parentheses squared plus 6 open parentheses 3 close parentheses squared plus a x plus 2 equals 14 space space space 81 minus 108 plus 54 plus a open parentheses 3 close parentheses plus 2 equals 14 space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space 29 plus 3 a equals 14 space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space 3 a equals negative 15 space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space a equals negative 5 end style 

Jadi, nilai begin mathsize 14px style a end style adalah begin mathsize 14px style negative 5 end style.

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Hasil dan sisa pembagian f(x)=x4+2x3−2x2+x+8 oleh (x+2) berturut-turut ....

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