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If f(x) = ax^4 – 4x^2 + ax – 3, then f(b) – f(-b) will equal:

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If f(x) = ax^4 – 4x^2 + ax – 3, then f(b) – f(-b) will equal: [#permalink]

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Tough and Tricky questions: Algebra.



If \(f(x) = ax^4 – 4x^2 + ax – 3\), then \(f(b) – f(-b)\) will equal:


A. 0

B. \(2ab\)

C. \(2ab^4 – 8b^2 – 6\)

D. \(-2ab^4 + 8b^2 + 6\)

E. \(2ab^4 – 8b^2 + 2ab – 6\)


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[Reveal] Spoiler: OA

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Re: If f(x) = ax^4 – 4x^2 + ax – 3, then f(b) – f(-b) will equal: [#permalink]

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New post 06 Nov 2014, 00:58
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Bunuel wrote:

Tough and Tricky questions: Algebra.



If f(x) = ax^4 – 4x^2 + ax – 3, then f(b) – f(-b) will equal:

A. 0
B. 2ab
C. 2ab^4 – 8b^2 – 6
D. -2ab^4 + 8b^2 + 6
E. 2ab^4 – 8b^2 + 2ab – 6

Kudos for a correct solution.


f(b)= ab^4 – 4b^2 + ab – 3 ----------------- 1)
f(-b)= ab^4 – 4b^2 - ab – 3 -------------------2)

1-2, will give us f(b)-f(-b)= 2ab
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Re: If f(x) = ax^4 – 4x^2 + ax – 3, then f(b) – f(-b) will equal: [#permalink]

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New post 06 Nov 2014, 14:29
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Bunuel wrote:

Tough and Tricky questions: Algebra.



If f(x)=ax^4–4x^2+ax–3, then f(b) – f(-b) will equal:

A. 0
B. 2ab
C. 2ab^4 – 8b^2 – 6
D. -2ab^4 + 8b^2 + 6
E. 2ab^4 – 8b^2 + 2ab – 6

Kudos for a correct solution.



f(x)=ax^4 – 4x^2 + ax – 3

f(b) = ab^4 – 4b^2 + ab – 3
f(-b) = ab^4 – 4b^2 - ab – 3

f(b) - f(-b) = ab^4 – 4b^2 + ab – 3 - ab^4 + 4b^2 + ab + 3
=2ab

Answer B
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Re: If f(x) = ax^4 – 4x^2 + ax – 3, then f(b) – f(-b) will equal: [#permalink]

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New post 06 Nov 2014, 18:58
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Bunuel wrote:

Tough and Tricky questions: Algebra.



If f(x) = ax^4 – 4x^2 + ax – 3, then f(b) – f(-b) will equal:

A. 0
B. 2ab
C. 2ab^4 – 8b^2 – 6
D. -2ab^4 + 8b^2 + 6
E. 2ab^4 – 8b^2 + 2ab – 6

Kudos for a correct solution.



\(f(x) = ax^4 - 4x^2 + ax - 3\)

\(f(b) = ab^4 - 4b^2 + ab - 3\)

\(f(-b) = a(-b)^4 - 4(-b)^2 + a(-b) - 3\)
\(f(-b) = ab^4 - 4b^2 - ab - 3\)

\(f(b) - f(-b) = [ab^4 - 4b^2 + ab - 3] - [ab^4 - 4b^2 - ab - 3]\)
\(f(b) - f(-b) = ab^4 - 4b^2 + ab- 3 - ab^4 + 4b^2+ ab + 3\)
\(f(b) - f(-b) = ab + ab\)
\(f(b) - f(-b) = 2ab\)

Answer is B

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Re: If f(x) = ax^4 – 4x^2 + ax – 3, then f(b) – f(-b) will equal: [#permalink]

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New post 09 Nov 2014, 23:16
\(f(x) = ax^4 – 4x^2 + ax – 3\)

For all even powers, sign would remain the same. For all odd powers, sign would change

\(f(b) - f(-b) = ab^4 - 4b^2 + ab - 3 - (ab^4 - 4b^2 - ab - 3) = 2ab\)

Answer = B
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Re: If f(x) = ax^4 – 4x^2 + ax – 3, then f(b) – f(-b) will equal: [#permalink]

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New post 08 Feb 2018, 06:37
I do not understand why does a(-b)^4 become ab^4 ??
it has to be -ab^4, doesn't it ?
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Re: If f(x) = ax^4 – 4x^2 + ax – 3, then f(b) – f(-b) will equal: [#permalink]

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New post 08 Feb 2018, 07:18
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Substitue the b with any negative number and make that number to the power of 4 and solve for it. You will get a positive figure, as any number to the power of even number will result a positive figure


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Re: If f(x) = ax^4 – 4x^2 + ax – 3, then f(b) – f(-b) will equal: [#permalink]

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New post 09 Feb 2018, 16:56
If you look at just -3 then

-3 - (-3) = 0

C, D, and E are out

From there, you can solve until you realize it does not = 0



Bunuel wrote:

Tough and Tricky questions: Algebra.



If \(f(x) = ax^4 – 4x^2 + ax – 3\), then \(f(b) – f(-b)\) will equal:


A. 0

B. \(2ab\)

C. \(2ab^4 – 8b^2 – 6\)

D. \(-2ab^4 + 8b^2 + 6\)

E. \(2ab^4 – 8b^2 + 2ab – 6\)


Kudos for a correct solution.
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Re: If f(x) = ax^4 – 4x^2 + ax – 3, then f(b) – f(-b) will equal: [#permalink]

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New post 11 Feb 2018, 00:43
gmatmo wrote:
I do not understand why does a(-b)^4 become ab^4 ??
it has to be -ab^4, doesn't it ?


hi gmatmo

\((-b)^4=-b*-b*-b*-b\).

In your opinion what should be the result of this multiplication?
Re: If f(x) = ax^4 – 4x^2 + ax – 3, then f(b) – f(-b) will equal:   [#permalink] 11 Feb 2018, 00:43
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