What number should be added to 2x3 3x2 8x so that the resulting polynomial leaves a remainder 10 when divided by 2x 1?

Sum

What number must be added to 2x3 – 7x2 + 2x so that the resulting polynomial leaves the remainder – 2 when divided by 2x – 3?

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Solution

Let a be added to 2x3 – 7x2 + 2x dividing it by 2x – 3, then

`2x - 3")"overline(2x^3 - 7x^2 + 2x + a)"(x^2 - 2x - 2`
             2x3 – 3x2 
             –    +                          
                   –4x2 + 2x
                   –4x2 + 6x
                   +      –                  
                           –4x + a
                           –4x + 6
                           +    –             
                              a – 6           
But remainder is –2, then
a – 6 = –2
⇒ a = –2 + 6
⇒ a = 4
Hence 4 is to be added.

Concept: Remainder Theorem

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What number should be added to 2x3 3x2 8x so that the resulting polynomial leaves a remainder 10 when divided by 2x 1?

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Updated On: 27-06-2022

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Text Solution

Answer : k = 7

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What number should be added to 2x3 3x2 8x so that the resulting polynomial leaves a remainder 10 when divided by 2x 1?

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What must be added to the polynomial 2x3 so that it leaves a remainder 10 when divided by 2x 1?

7 must be added to the polynomial 2x^3 - 3x^2 - 8x so that it leaves a remainder 10 when divided by 2x + 1. Thus, the number that must be added would be 7.

What should be added in 2x 1?

Let us assume that on the addition of a in 2x+1 the result is obtained as 1. Hence, -2x should be added to 2x+1 to get the result 1.