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Which one is the factor of given polynomial - x3 - 22 x2 + 143x -120 
1. (x - 1)
2. (x + 1) 
3. (x - 2)
4. (x - 3)

1 Answer

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Best answer
Correct Answer - Option 1 : (x - 1)

Calculation:

Option A:

P(x) = x - 1

x - 1 = 0

x = 1

f(x) = - x3 - 22x2 + 143x -120 

⇒ f(1) = - 1 (1)3 - 22 (1)2 + 143 (1) - 120

⇒ f(1) = - 1 - 22 + 143 - 120 

⇒ f(1) = - 143 + 143 = 0

∴  (x - 1) is a factor of (- x3 - 22x2 + 143x -120)

Option B:

P(x) = x + 1 

x + 1 = 0

x = - 1

f(x) = - x3 - 22x2 + 143x -120 

⇒ f(-1) = - 1 (-1)3 - 22 (-1)2 + 143 (-1) - 120

⇒ f(-1) = 1 - 22 - 143 - 120 

⇒ f(-1) = 1 - 285 = -284

∴ (x + 1) is not a factor of (- x3 - 22x2 + 143x - 120)

Option C:

P(x) = x - 2 

x - 2 = 0

x = 2

f(x) = - x3 - 22x2 + 143x -120 

⇒ f(2) = -1(2)3 - 22(2)2 + 143(2) - 120

⇒ f(2) = -8 - 88 + 286 - 120 

⇒ f(2) = -216 + 286 = 70

∴ (x - 2) is not a factor of (- x3 - 22x2 + 143x -120)

Option D:

P(x) = x - 3

x - 3 = 0

x = 3

f(x) = - x3 - 22x2 + 143x -120 

⇒ f(3) = -1(3)3 - 22(3)2 + 143(3) - 120

⇒ f(3) = - 27 - 198 + 429 - 120 

⇒ f(3) = -345 + 429

⇒ f(3) = 84

∴ (x - 3) is not a factor of (- x3 - 22x2 + 143x -120)

The correct option is 1 i.e. (x - 1)

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