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 Algebra Pre-Algebra and Basic Algebra Math Forum

 February 15th, 2018, 06:51 AM #1 Senior Member   Joined: Nov 2010 From: Indonesia Posts: 2,001 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: 2,838 Thanks: 1481 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: 7,618 Thanks: 2608 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: 14,124 Thanks: 1003 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: 20,373 Thanks: 2010 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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 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. Tags polynomial Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post Nienna426 Number Theory 4 April 18th, 2015 08:14 PM jiasyuen Math 1 February 5th, 2015 08:39 AM king.oslo Algebra 6 August 27th, 2013 06:11 AM link107 Algebra 12 January 31st, 2012 09:28 PM condemath Algebra 3 September 20th, 2011 08:34 PM

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