We can think of `(6x^2+6+7x)/(2x+1)` as (6x2 + 7x + 6) ÷ (2x + 1)

Once again we are dividing a polynomial of degree 2 by a polynomial of lower degree (1). This is algebraic long division.


Step 1: 6x2 ÷ 2x = 3x

So we write the following, using (3x)(2x + 1) = 6x2 + 3x for the second row:

Division of polynomials

Step 2: We subtract 6x2 + 3x from the first row:

Division of polynomials

Step 3: Bring down the 6:

Division of polynomials

Step 4: Divide 4x by 2x. Our answer is 2 and we multiply 2(2x + 1) to get the 4th row.

Division of polynomials

Step 5: Subtract, and we are left with 4.

Division of polynomials

So the answer is:

`(6x^2+6+7x)/(2x+1)=3x+2+4/(2x+1)`

NOTE: Some people prefer to write the problem with all the x2's, x's and units in line, as follows:

Division of polynomials

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