We are dividing a polynomial of degree 2 by a polynomial of degree 1. This is algebraic long division.

Step 1: We look at the first term of (3x2 − 11x − 4) and the first term of (x − 4).

Divide as follows: 3x2 ÷ x = 3x

We write 3x at top of our long division and multiply (3x)(x − 4) = 3x2 − 12x to give the second row of our solution.

Division of polynomials

Step 2: Subtracting the second row from the first gives:

Division of polynomials

Be careful with

-11x − (-12x) = -11x + 12x = x

Step 3: Bring down the -4 from the first row:

Division of polynomials

Step 4: Divide x (in the 3rd row) by x from the (x − 4) in the question. Our answer is 1 and we write "+ 1" at the top of our long division.

Next, multiply (1) by (x − 4) to get the 4th row.

Division of polynomials

Step 5: Subtract the 4th row from the 3rd:

Division of polynomials

So (3x2 − 11x − 4) ÷ (x − 4) = 3x + 1

You can check your answer by multiplying (3x + 1) by (x − 4) and you'll get (3x2 − 11x − 4).