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If a^3 a^2 a + 1 = 0, what is the product of all possible values o

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Carcass
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If a^3 a^2 a + 1 = 0, what is the product of all possible values o [#permalink] New post   14 May 2022, 08:15
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If a3−a2−a+1=0, what is the product of all possible values of a?

A. -1
B. 0
C. 1
D. 2
E. 4
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A
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GreenlightTestPrep
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Re: If a^3 a^2 a + 1 = 0, what is the product of all possible values o [#permalink] New post   14 May 2022, 11:12
Carcass wrote:
If a3−a2−a+1=0, what is the product of all possible values of a?

A. -1
B. 0
C. 1
D. 2
E. 4

We can factor the left side in parts.

Given: a³ − a² − a + 1 = 0

Factor in parts: a²(a − 1) - 1(a - 1) = 0

Combine to get: (a² - 1)(a − 1) = 0

Since the first expression (and brackets) is a difference of squares, we can factor it as follows: (a + 1)(a - 1)(a - 1) = 0

There are two unique solutions: a = 1 and a = -1, which means the product of all possible values of a = (1)(-1) = -1

Answer: A
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Re: If a^3 a^2 a + 1 = 0, what is the product of all possible values o [#permalink]
14 May 2022, 11:12
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