Q. Divide. If there is a remainder, include it as a simplified fraction.(5m3−36m2−81m)÷(m−9)______
Divide by First Term: We will use polynomial long division to divide (5m3−36m2−81m) by (m−9). First, we divide the first term of the dividend, 5m3, by the first term of the divisor, m, to get the first term of the quotient. 5m3÷m=5m2
Subtract and Multiply: Now, we multiply the entire divisor (m−9) by the first term of the quotient (5m2) and subtract the result from the dividend.(5m2)⋅(m−9)=5m3−45m2Subtract this from the dividend:(5m3−36m2−81m)−(5m3−45m2)=9m2−81m
Divide New Term: Next, we divide the first term of the new dividend, 9m2, by the first term of the divisor, m, to get the next term of the quotient.9m2÷m=9m
Subtract and Multiply: We multiply the entire divisor (m−9) by the new term of the quotient (9m) and subtract the result from the new dividend.(9m)×(m−9)=9m2−81mSubtract this from the new dividend:(9m2−81m)−(9m2−81m)=0
Final Quotient: Since we have no remainder, the division process is complete. The quotient is the sum of the terms we found: 5m2+9m
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