Question

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An unknown polynomial yields a remainder of 2 upon division by x-1, and a remainder of 1 upon division by
X-2. If this polynomial is divided by (x - 1)(x-2), then the remainder is -
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Answer 1

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Answer 2

Answer:

hey mate here is ur answer

Please find below the solution to the asked query:

P ÷ (x – 1) remainder 2 

P ÷ (x – 2) remainder 1 

the difference in divisisor and remainder is 

first case (x – 1) – 2 = (x – 3) 

second case (x – 2) – 1 = (x – 3) 

is same 

so least polynomial is 

(LCM of divisors) – difference 

= (x – 1)(x – 2) – (x – 3) 

= x^2 – 3x + 2 – x + 3 

= (x^2 – 4x + 5) 

so remainder when 

(x^2 – 4x + 5) ÷ (x – 1)(x – 2) 

= (x^2 – 4x + 5) ÷ (x^2 – 3x + 2) 

quotient 1 and remainder 

= (x^2 – 4x + 5) – (x^2 – 3x + 2) 

= – x + 3 

= 3 – x 

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