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# When f(x)=ax^2+bx+c (a≠0), is x+1 a factor of f(x)?

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
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GMAT 1: 760 Q51 V42
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When f(x)=ax^2+bx+c (a≠0), is x+1 a factor of f(x)?  [#permalink]

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26 Sep 2018, 05:03
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55% (hard)

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45% (01:26) correct 55% (01:51) wrong based on 48 sessions

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[Math Revolution GMAT math practice question]

When $$f(x)=ax^2+bx+c (a≠0)$$, is $$x+1$$ a factor of $$f(x)?$$

$$1) f(1)=0$$
$$2) f(-1)=0$$

_________________
MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only $79 for 1 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" NUS School Moderator Joined: 18 Jul 2018 Posts: 1024 Location: India Concentration: Finance, Marketing WE: Engineering (Energy and Utilities) Re: When f(x)=ax^2+bx+c (a≠0), is x+1 a factor of f(x)? [#permalink] ### Show Tags 26 Sep 2018, 05:20 If x+1 a factor of f(x) or otherwise when x equals -1, f(x) should be zero. Clearly B is sufficient. B is the answer Posted from my mobile device _________________ Press +1 Kudos If my post helps! GMATH Teacher Status: GMATH founder Joined: 12 Oct 2010 Posts: 935 Re: When f(x)=ax^2+bx+c (a≠0), is x+1 a factor of f(x)? [#permalink] ### Show Tags 26 Sep 2018, 09:17 MathRevolution wrote: [Math Revolution GMAT math practice question] When $$f(x)=ax^2+bx+c (a≠0)$$, is $$x+1$$ a factor of $$f(x)?$$ $$1) f(1)=0$$ $$2) f(-1)=0$$ $$a \ne 0$$ $$a{x^2} + bx + c\,\,\mathop = \limits^? \,\,\left( {x + 1} \right) \cdot p\left( x \right)\,\,\,\,\,\, \Leftrightarrow \,\,\,\,a{\left( { - 1} \right)^2} + b\left( { - 1} \right) + c\,\,\mathop = \limits^? \,\,0\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,\boxed{b\,\,\mathop = \limits^? \,\,a + c}$$ $$\left( 1 \right)\,\,\,a + b + c = 0\,\,\,\,\,\left\{ \begin{gathered} \,{\text{Take}}\,\,\left( {a,b,c} \right) = \left( {2,0, - 2} \right)\,\,\,\, \Rightarrow \,\,\,\left\langle {{\text{YES}}} \right\rangle \,\,\,\left( * \right)\, \hfill \\ \,{\text{Take}}\,\,\left( {a,b,c} \right) = \left( {1,2, - 3} \right)\,\,\,\,\, \Rightarrow \,\,\,\left\langle {{\text{NO}}} \right\rangle \,\,\,\left( {**} \right)\,\, \hfill \\ \end{gathered} \right.$$ $$\left( * \right)\,\,\,2{x^2} - 2 = 2\left( {x + 1} \right)\left( {x - 1} \right) = \left( {x + 1} \right) \cdot p\left( x \right)\,\,\,,\,\,\,\,p\left( x \right) = 2\left( {x - 1} \right)$$ $$\left( {**} \right)\,\,{x^2} + 2x - 3 = \left( {x - 1} \right)\left( {x + 3} \right)$$ $$\left( 2 \right)\,\,a{\left( { - 1} \right)^2} + b\left( { - 1} \right) + c = 0\,\,\,\, \Rightarrow \,\,\,\,\left\langle {{\text{YES}}} \right\rangle$$ The correct answer is therefore (B). This solution follows the notations and rationale taught in the GMATH method. Regards, Fabio. _________________ Fabio Skilnik :: GMATH method creator (Math for the GMAT) Our high-level "quant" preparation starts here: https://gmath.net Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 8005 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: When f(x)=ax^2+bx+c (a≠0), is x+1 a factor of f(x)? [#permalink] ### Show Tags 28 Sep 2018, 00:38 => Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution. The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question. $$x+1$$ is a factor of $$f(x)$$ precisely when $$f(x) = (x+1)(ax+b)$$ for some numbers $$a$$ and $$b$$. This occurs when $$f(-1) = 0$$, but not necessarily when $$f(1) = 0$$. Thus, only condition 2) is sufficient. Therefore, B is the answer. Answer: B If the original condition includes “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations” etc., one more equation is required to answer the question. If each of conditions 1) and 2) provide an additional equation, there is a 59% chance that D is the answer, a 38% chance that A or B is the answer, and a 3% chance that the answer is C or E. Thus, answer D (conditions 1) and 2), when applied separately, are sufficient to answer the question) is most likely, but there may be cases where the answer is A,B,C or E. _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$79 for 1 month Online Course"
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Re: When f(x)=ax^2+bx+c (a≠0), is x+1 a factor of f(x)?   [#permalink] 28 Sep 2018, 00:38
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