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Sisa pembagian begin mathsize 14px style straight x to the power of 2014 minus Ax to the power of 2015 plus Bx cubed minus 1 end style oleh begin mathsize 14px style straight x squared minus 1 end style adalah -x + B. Nilai 2A + B adalah ....

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A. Rizky

Master Teacher

Mahasiswa/Alumni Universitas Negeri Malang

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Pembahasan

begin mathsize 14px style box enclose Ingat space pada space suku space banyak space berlaku space colon  straight f open parentheses straight x close parentheses equals straight p open parentheses straight x close parentheses straight h open parentheses straight x close parentheses plus straight s open parentheses straight x close parentheses end enclose    straight x to the power of 2014 minus Ax to the power of 2015 plus Bx cubed minus 1 equals open parentheses straight x squared minus 1 close parentheses straight h open parentheses straight x close parentheses minus straight x plus straight B  straight x to the power of 2014 minus Ax to the power of 2015 plus Bx cubed minus 1 equals open parentheses straight x plus 1 close parentheses open parentheses straight x minus 1 close parentheses straight h open parentheses straight x close parentheses minus straight x plus straight B    Substitusi space straight x space equals space minus 1  open parentheses negative 1 close parentheses to the power of 2014 minus straight A open parentheses negative 1 close parentheses to the power of 2015 plus straight B open parentheses negative 1 close parentheses cubed minus 1 equals open parentheses negative 1 plus 1 close parentheses open parentheses negative 1 minus 1 close parentheses straight h open parentheses straight x close parentheses minus open parentheses negative 1 close parentheses plus straight B  1 plus straight A minus straight B minus 1 equals 1 plus straight B  straight A minus 2 straight B equals 1 space...... left parenthesis 1 right parenthesis    Substitusi space straight x space equals space 1  open parentheses 1 close parentheses to the power of 2014 minus straight A open parentheses 1 close parentheses to the power of 2015 plus straight B open parentheses 1 close parentheses cubed minus 1 equals open parentheses 1 plus 1 close parentheses open parentheses 1 minus 1 close parentheses straight h open parentheses straight x close parentheses minus 1 plus straight B  1 minus straight A plus straight B minus 1 equals negative 1 plus straight B  minus straight A equals negative 1 rightwards double arrow straight A equals 1 space..... left parenthesis 2 right parenthesis    Substitusi space persamaan space left parenthesis 2 right parenthesis space ke space persamaan space left parenthesis 1 right parenthesis space colon  1 minus 2 straight B equals 1 space  minus 2 straight B equals 0 space  straight B equals 0 space  Jadi comma space 2 straight A space plus space straight B space equals space 2 end style

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Sisa pembagian p(x)=x3+ax2+4x+2b+1 oleh x2+4 adalah b−3a. Jika p(x) habis dibagi oleh x+1, maka a2+b=...

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