Question

Divide. Divide \(4+11 q+6 q^{2}\) by \(2 q+1\)

Short answer

The quotient after dividing \(4+11q+6q^2\) by \(2q+1\) is \(3q + 2\).

Step-by-step solution

Set up the long division

First, arrange the equation so that the divisor \(2q + 1\) is on the outside of the division symbol and the dividend \(4+11q+6q^2\) is under the division symbol. Make sure to write the terms of the dividend in decreasing order of the terms' degrees (degree of a term is the power of variable in the term), so instead of \(4+11q+6q^2\), write it as \(6q^2 + 11q + 4\).

Divide the highest degree terms

Divide \(6q^2\), the term with the highest degree in the dividend, by \(2q\), the term with the highest degree in the divisor. The result of this division \(3q\), is the first term of the quotient.

Multiply and Subtract

Multiply the divisor \(2q + 1\) by the first term of the quotient \(3q\). Subtract the result from the dividend and bring down the next term. This will provide you a new polynomial.

Repeat the Process

Apply the same division process to the new polynomial. Divide the highest degree term of the new polynomial by the highest degree term of the divisor. The result of this will be the next term of the quotient. Continue this process until every term in the dividend has been brought down.

Write down the final quotient

All the terms obtained from each division make up the final quotient.