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February 15th, 2018, 06:51 AM  #1 
Senior Member Joined: Nov 2010 From: Indonesia Posts: 1,817 Thanks: 123 Math Focus: Trigonometry and Logarithm  [ASK] About Polynomial
A polynomial f(x) = $\displaystyle 2x^35x^2+ax+18$ is divisible by (x  3). The result of that polynomial f(x) divided by (x  1) is .... A. $\displaystyle 2x^27x+2$ B. $\displaystyle 2x^2+7x2$ C. $\displaystyle 2x^27x2$ D. $\displaystyle x^26x2$ E. $\displaystyle x^26x+3$ I got a + 3 = 6 and so a = 9 and f(x) = $\displaystyle 2x^35x^29x+18$, but when I divided it with x  1 I got $\displaystyle x^23x+6$ with the remainder 24. I'm quite sure that the question isn't wrong since it's in a national level exam, but where did I go wrong? 
February 15th, 2018, 07:06 AM  #2 
Math Team Joined: Jul 2011 From: Texas Posts: 2,723 Thanks: 1376 
Must be an error in the question somewhere ... $f(3) = 0 \implies a = 9 \implies f(1) = 6 \implies f(x)$ is not divisible by $x1$. 
February 15th, 2018, 07:24 AM  #3 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,232 Thanks: 2411 Math Focus: Mainly analysis and algebra 
If the leading coefficient of both divisor and dividend are not equal, the result cannot have a leading coefficient of 1. There's clearly a problem with your division.

February 15th, 2018, 12:19 PM  #4 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 11,847 Thanks: 766 
Long division: (2x^3  5x^2 + ax + 18 ) / (x  3) = 2x^2 + x + 3 with remainder = 27 Last edited by Denis; February 15th, 2018 at 12:42 PM. 
February 15th, 2018, 02:03 PM  #5 
Global Moderator Joined: Dec 2006 Posts: 18,702 Thanks: 1527 
I suspect that the question should be asking for the result of the polynomial $f(x)$ divided by $(x + 1)$ instead of $(x  1)$. Dividing $2x^3  5x^2  9x + 18$ by $(x + 1)$ gives $2x^2  7x  2$ (with remainder 20), which corresponds to answer choice C. 
February 15th, 2018, 05:29 PM  #6 
Senior Member Joined: Nov 2010 From: Indonesia Posts: 1,817 Thanks: 123 Math Focus: Trigonometry and Logarithm  That's a possible reason since the paper was photocopied and sometimes the vertical line on the plus sign doesn't show up thus making people think it is a minus sign.


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