Divide Using Long Polynomial Division (4x+7)/(3x-2)

Problem

(4*x+7)/(3*x−2)

Solution

1. Divide the leading term of the numerator by the leading term of the denominator to find the first term of the quotient.

(4*x)/(3*x)=4/3

2. Multiply the entire divisor by this quotient term.

4/3*(3*x−2)=4*x−8/3

3. Subtract this result from the original numerator to find the remainder.

(4*x+7)−(4*x−8/3)=7+8/3

4. Simplify the remainder by finding a common denominator.

21/3+8/3=29/3

5. Write the final result in the form Quotient+Remainder/Divisor

4/3+29/3/(3*x−2)

Final Answer

(4*x+7)/(3*x−2)=4/3+29/(3*(3*x−2))

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