The smallest integer that can be added to -2m² - m + m² + 1 to make it completely divisible by m + 1 is -5
Step-by-step explanation:
A number is divisible by a number when divided by it and the remainder is zero (20 is divisible by 4 because 20 ÷ 4 = 5 + remainder zero)
To check if -2m³ - m + m² + 1 can be divisible by m + 1 do that:
We need to find the smallest integer that can be added to -2m³ - m + m² + 1 to make it completely divisible by m + 1
Assume that the smallest number is k
∴ The dividend is -2m² - m + m² + 1 + k
∵ The divisor is m + 1
- Equate the divisor by 0 to find the value of m
∵ m + 1 = 0
- Subtract 1 from both sides
∴ m = -1
Substitute the value of m in -2m² - m + m² + 1 + k to find its value
∵ -2(-1)³ - (-1) + (-1)² + 1 + k = -2(-1) + 1 + 1 + 1 + k
∴ -2(-1) + 1 + 1 + 1 + k = 2 + 1 + 1 + 1 + k
- Add like terms
∴ 2 + 1 + 1 + 1 + k = 5 + k
∴ -2m² - m + m² + 1 + k = 5 + k at m = -1
∵ -2m² - m + m² + 1 + k is divisible by m + 1
∴ The value of -2m² - m + m² + 1 + k = 0 at m = -1
- Equate 5 + k by 0
∴ 5 + k = 0
- Subtract 5 from both sides
∴ k = -5
Substitute the value of k in -2m² - m + m² + 1 + k
∵ -2m² - m + m² + 1 + (-5)
- Add like term
∴ -2m² - m + m² - 4
- To check your answer substitute m by -1 the answer must be 0
∵ -2(-1)³ - (-1) + (-1)² - 4 = 2 + 1 + 1 - 4 = 0
∴ The smallest integer can be added is -5
The smallest integer that can be added to -2m² - m + m² + 1 to make it completely divisible by m + 1 is -5
Learn more:
You can learn more about the divisibility in brainly.com/question/10941043
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