# Long Division with Remander & Factor Theorems

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Last updated 5 years ago

Discipline:
Math
Subject:
Number Operations
10   REMANDER THEROMIf you divide a polynomial, f(x), by a linear factor of the from:(x-a),the remander will equal:f(a)When -3 is inserted as x it will give the same remander as by using long division and or synthetic division. FACTOR THEROM(x-a) is a factor of P(x) if and only if P(a) is zero.Where: P(x) is a polynomialP(a) is a remander "a" is any number

Long Divsion with remander & Factor Theorems

Factor Therom

Remander Therom

Long Division

1) Set up for long division if needed.2) If there are any powers missing; add in the missing power with a zero3) Ignore the other terms and look just at the leading x of the divisor and the leading 8x^3 of the dividend.4) Divide the leading 8x^3 inside by the leading x in front to get an 8x^2.Then put the 8x^2 on top5) Now take the 8x^2, and multiply it through the divisor, x-1. First, multiply the 8x^2 (on top) by the x (on the "side"), and carry the 8x^3 underneath the original 8x^3.6) Then multiply the 8x^2 (on top) by the -1 (on the "side"), and carry the -8x^2 underneath the -10x^27) From here subtract the polynomials. Make sure to change all the signs in the second line. 8) The first term should cancel out. Then end up with -2x^29) Now drop down the next leading term which would be -x.10) Repeat steps 3-8 (pattern based) untill there are no more terms to bring down.11) When finished the answer is on the top of the problom.Answer: 8x^2-2x-312) If the remander is not zero then it must be added to the top if a special way. Say if the remander was 2 instead of zero; it must be writen like this: 8x^2-2x-3+2/x-1