Question

what number should be added to 2x^3-3x^2-8x so that the resultant polynomial leaves remainder 10when divided by (2x+1).

Answer 1

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

Answer 2

Answer:

• 7 must be added.

Step-by-step explanation:

f(x) = 2x³ - 3x² - 8x

• 2x³ - 3x² - 8x + k

∘ (2x + 1) = 0, x = -1/2

f(-1/2) :

› 2(-1/2)³ - 3(-1/2)² - 8(-1/2) + k = 10

› 2(-1/8) - 3(1/4) + 4 + k = 10

› -1/4 - 3/4 + k = 10 - 4

› -4/4 + k = 6

› -1 + k = 6

› k = 6 + 1

∴ k = 7