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

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Math Expert
Joined: 02 Sep 2009
Posts: 60627
If f(x) = ax^4 – 4x^2 + ax – 3, then f(b) – f(-b) will equal:  [#permalink]

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05 Nov 2014, 08:38
1
5
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Difficulty:

35% (medium)

Question Stats:

69% (01:33) correct 31% (02:00) wrong based on 220 sessions

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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. $$2ab^4 – 8b^2 + 2ab – 6$$

Kudos for a correct solution.

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Joined: 13 Jun 2013
Posts: 253
Re: If f(x) = ax^4 – 4x^2 + ax – 3, then f(b) – f(-b) will equal:  [#permalink]

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06 Nov 2014, 01:58
2
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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Joined: 10 Jul 2014
Posts: 40
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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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06 Nov 2014, 15:29
1
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

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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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06 Nov 2014, 19:58
1
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.

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

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

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

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

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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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10 Nov 2014, 00:16
1
$$f(x) = ax^4 – 4x^2 + ax – 3$$

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

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

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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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08 Feb 2018, 07:37
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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Joined: 30 Jan 2018
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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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08 Feb 2018, 08:18
1
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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Joined: 29 Jan 2017
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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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09 Feb 2018, 17:56
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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Joined: 25 Feb 2013
Posts: 1156
Location: India
GPA: 3.82
Re: If f(x) = ax^4 – 4x^2 + ax – 3, then f(b) – f(-b) will equal:  [#permalink]

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11 Feb 2018, 01:43
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?
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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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02 Dec 2019, 00:06
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Re: If f(x) = ax^4 – 4x^2 + ax – 3, then f(b) – f(-b) will equal:   [#permalink] 02 Dec 2019, 00:06
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