What number should be added to 2x³ 3x² 8x so that the resulting polynomial leaves the 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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8x là gì - Nghĩa của từ 8x

8x có nghĩa làTất cả học sinh lớp 8 [các cô gái và các chàng trai] đều là những con điếm, điều này có nghĩa là nếu bạn muốn nói chuyện với một học sinh ...

Là gì Nghĩa của từ 8x

Answer:

The number that should be added is 7 .

Step-by-step explanation :

Given as :

The polynomial expression 2 x³ - 3 x² - 8 x

Remainder = 10

The polynomial is divided by 2 x + 1

Let The number to be added = n

According to question

∵ 2 x³ - 3 x² - 8 x is divided by 2 x + 1

So, x = - \dfrac{1}{2}  is the factor

So, remainder = 2 x³ - 3 x² - 8 x  + number

Or, 10 = 2 [ - \dfrac{1}{2} ]³ - 3 [ - \dfrac{1}{2} ]² - 8 [ - \dfrac{1}{2}  ] + n

Or, 10 = \dfrac{-1}{4} - \dfrac{3}{4} + 4 + n

Or, 10 - 4 = n - 1

Or, n = 6 + 1

∴   n = 7

So, The number that should be added = n = 7

Hence, The number that should be added is 7 .Answer

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Updated On: 27-06-2022

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Text Solution

Answer : k = 7

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