What must be added to the polinomial 2x³ - 3x² - 8x, so that it leaves a reminder 10 when divided by 2x + 1?
Answers
Answered by
2
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}
2
1
is the factor
So, remainder = 2 x³ - 3 x² - 8 x + number
Or, 10 = 2 ( - \dfrac{1}{2}
2
1
)³ - 3 ( - \dfrac{1}{2}
2
1
)² - 8 ( - \dfrac{1}{2}
2
1
) + n
Or, 10 = \dfrac{-1}{4}
4
−1
- \dfrac{3}{4}
4
3
+ 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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Answered by
3
Answer:
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