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 February 15th, 2018, 06:51 AM #1 Senior Member     Joined: Nov 2010 From: Indonesia Posts: 2,000 Thanks: 132 Math Focus: Trigonometry [ASK] About Polynomial A polynomial f(x) = $\displaystyle 2x^3-5x^2+ax+18$ is divisible by (x - 3). The result of that polynomial f(x) divided by (x - 1) is .... A. $\displaystyle 2x^2-7x+2$ B. $\displaystyle 2x^2+7x-2$ C. $\displaystyle 2x^2-7x-2$ D. $\displaystyle x^2-6x-2$ E. $\displaystyle x^2-6x+3$ I got a + 3 = -6 and so a = -9 and f(x) = $\displaystyle 2x^3-5x^2-9x+18$, but when I divided it with x - 1 I got $\displaystyle x^2-3x+6$ 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: 2,767 Thanks: 1422 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 $x-1$. Thanks from v8archie
 February 15th, 2018, 07:24 AM #3 Math Team   Joined: Dec 2013 From: Colombia Posts: 7,355 Thanks: 2469 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: 13,103 Thanks: 907 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: 19,505 Thanks: 1741 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
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Quote:
 Originally Posted by skipjack I suspect that the question should be asking for the result of the polynomial $f(x)$ divided by $(x + 1)$ instead of $(x - 1)$.
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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