We can divide the given expression using synthetic division. Here are the steps:
1. List down the numerical coefficients of the numerator horizontally in order from the highest to the lowest degree. Take note that there is no m² in the expression, hence, assume 0 as the numerical coefficient for m².
2. Equate the denominator to m = 1. 1 will be our divisor.
See the arrangements for steps 1 and 2 below.
3. Bring down the first numerator which is 4 to the third row. Multiply this to the divisor 1. Add the result to the next numerator that is zero.
4. Upon adding, the result is still 4. Multiply this again to the divisor and add the result to the next numerator which is 1.
5. The result is 5. Multiply this to the divisor 1 and add the result to the last numerator which is -5.
The result is zero.
We have completed the synthetic division.
To interpret this, first, we can see that in the last column, the last row, the result is zero. This means that there is no remainder in the division.
Second, we see 4, 4, 5. These are the numerical coefficients of the quotient in exact order. The variables of these numbers will be the highest degree minus 1. This means we're going to start with m².
So, the quotient of the polynomial and the binomial above is:
The quotient is 4m² + 4m + 5.