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Does f(x)=ax^4+bx^3+cx^2+dx+e have (x-2) as a factor?

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by Max@Math Revolution » Fri Feb 08, 2019 1:22 am

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B

C

D

E

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[GMAT math practice question]

Does f(x)=ax^4+bx^3+cx^2+dx+e have (x-2) as a factor?

1) f(2)=0
2) f(-2)=0
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Source: — Data Sufficiency |
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by Max@Math Revolution » Sun Feb 10, 2019 4:53 pm
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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.
The statement that f(x)=ax^4+bx^3+cx^2+dx+e has (x-2) as a factor is equivalent to saying f(x) = (x-2)g(x) for some function g(x). This is equivalent to the requirement that f(2) = 0.

Thus condition 1) is sufficient.

Condition 2)
If f(x) = (x-2)(x+2)(x-1)(x+1), then f(x) has x-2 as a factor, The answer is 'yes'.
If f(x) = x(x+2)(x+1)(x-1), then f(x) doesn't have x-2 as a factor. The answer is 'no'.
Since condition 2) does not yield a unique answer, condition 2) is not sufficient.

Therefore, the answer is A.
Answer: A
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