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If (x-1) is a factor of (x^(3)-m), then ...

If `(x-1)` is a factor of `(x^(3)-m)`, then the value of m is :

A

`-6`

B

`-5`

C

1

D

3

Text Solution

AI Generated Solution

The correct Answer is:
To solve the problem, we need to determine the value of \( m \) given that \( (x-1) \) is a factor of \( (x^3 - m) \). ### Step-by-step Solution: 1. **Understanding the Factor Condition**: Since \( (x-1) \) is a factor of \( (x^3 - m) \), it means that when we substitute \( x = 1 \) into the polynomial \( x^3 - m \), the result should equal zero. This is based on the Factor Theorem. 2. **Substituting \( x = 1 \)**: We substitute \( x = 1 \) into the expression \( x^3 - m \): \[ 1^3 - m = 0 \] 3. **Calculating \( 1^3 \)**: We know that \( 1^3 = 1 \). So, we can rewrite the equation: \[ 1 - m = 0 \] 4. **Solving for \( m \)**: To isolate \( m \), we can rearrange the equation: \[ 1 = m \] 5. **Final Answer**: Therefore, the value of \( m \) is: \[ m = 1 \]
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ARIHANT SSC-ELEMENTS OF ALGEBRA-INTRODUCTORY EXERCISE - 13.1
  1. One of the factors of 3x^(3)+x^(2)-12x-4 is :

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  2. If (x^(100)+2x^(99)+k) is divisible by ( x+1 ) then the value of...

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  3. If (x-1) is a factor of (x^(3)-m), then the value of m is :

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  4. If the polynomial f(x) is such that f(-3)=0, then a factor of f(x) is ...

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  5. If x+1/x=2 then x^2+1/x^2 is equal to

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  6. If (x-(1)/(x))=4, then the value of (x^(2)+(1)/(x^(2))) is :

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  7. If (x+(1)/(x))=2sqrt3, then the value of (x^(3)-(1)/(x^(3))) is :

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  8. If (x+(1)/(x))=3, then the value of (x^(3)+(1)/(x^(3))) is equal to :

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  9. If (x+(1)/(x))=2, then the value of (x^(6)+(1)/(x^(6))) is :

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  10. If (x^(2)+(1)/(x^(2)))=6, then the value of (x+(1)/(x)) is :

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  11. if x^3-1/x^3=36 then find the value of x-1/x

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  12. If (x^(3)+(1)/(x^(3)))=2, then the value of (x+(1)/(x)) is :

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  13. If (x^(4)+(1)/(x^(4)))=34, then the value of (x-(1)/(x)) is :

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  14. If x^4+1/(x^4)=119 , find the value of x^3-1/(x^3)

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  15. If (3x-(2)/(x))=5, then the value of (9x^(2)-(4)/(x^(2))) is :

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  16. If m^(2)-4m+1=0, then the value of (m^(3)+(1)/(m^(3))) is :

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  17. If x+y=13 and xy = 40, then the value of (x^(2)+y^(2)) is :

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  18. If (x+y)=13 and xy=36, then the value of (x^(3)+y^(3)) is :

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  19. If (x+y)=13 and xy=36, then the value of (x^(3)+y^(3)) is :

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  20. If (x+y+z)=6 and (xy+yz+zx)=11, then the value of (x^(3)+y^(3)+z^(3)-3...

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