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705-805 Level|   Algebra|      
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Bunuel
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If a, b and c are integers and x^3 - x^2 - x + 1=(x + a)(x + b)(x + c) 14 Jun 2022, 05:15
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D
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75% (hard)

Question Stats:

43% (01:53) correct 57% (02:23) wrong based on 42 sessions

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If a, b and c are integers and \(x^3-x^2-x+1=(x + a) (x + b) (x + c)\). Is b = c?

(1) a < 0

(2) b > 0
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D
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Ajay5068
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If a, b and c are integers and x^3 - x^2 - x + 1=(x + a)(x + b)(x + c) 15 Jun 2022, 03:38
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Can anyone kindly explain the solution ??
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If a, b and c are integers and x^3 - x^2 - x + 1=(x + a)(x + b)(x + c) 15 Jun 2022, 22:08
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Simply the LHS and we will get
(X-1)(x+1)(x-1)
Now statement 1
If a is less than 0 then remaining b and c are not equal sufficient.
Statement 2
If b is more than zero then again a and c will be negetive and b and c will not be equal
Sufficient so ans D

Please correct if in error thanks

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If a, b and c are integers and x^3 - x^2 - x + 1=(x + a)(x + b)(x + c) 17 Jun 2022, 22:20
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Bunuel
If a, b and c are integers and \(x^3-x^2-x+1=(x + a) (x + b) (x + c)\). Is b = c?

(1) a < 0

(2) b > 0

Bunuel - can you provide a solution for this?
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If a, b and c are integers and x^3 - x^2 - x + 1=(x + a)(x + b)(x + c) 18 Jun 2022, 03:50
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Ajay5068
Can anyone kindly explain the solution ??
Simplifying the LHS of the equation:
(x^3 - x^2) - (x + 1) = x^2 (x-1) - 1 (x-1) = (x^2-1)(x-1) = (x-1)(x+1)(x-1)

So the entire equation now reads:
(x+1)(x-1)^2 = (x+a)(x+b)(x+c)
We need to answer if b=c, now after simplifying the equation we can figure out that a,b and c correspond to 1,-1 and -1 so b and c both have to be -1 for them to be equal. Let us now go to the statements

1) a<0
If a<0 and a,b,c are all integers, this means that a=-1, which means that either b or c will be -1 but not both so b is not equal to c in any situation.
SUFFICIENT

2) b>0
If b>0 and a,b,c are all integers, this means that b=+1, which means that both a and c are -1 so b is not equal to c.
SUFFICIENT

Answer - D
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