DIVISION OF POLYNOMIALS

DIVIDING BY A MONOMIAL

EXAMPLE 1

Divide

                       

LONG DIVISION OF POLYNOMIALS

STEP 1: Write the polynomials in the long-division format, expressing each in standard form.

STEP 2: Divide the first term of the divisor into the first term of the dividend. The result of this division is the first term of the quotient.

STEP 3: Multiply the first term of the quotient times every term in the divisor. Write this product under the dividend, aligning like terms.

STEP 4: Subtract this product from the dividend, and bring down the next term.

STEP 5: Using the result of Step 4 as a new dividend, and repeat Steps 2 through 4 until either the remainder is zero or the degree of the remainder is less than the degree of the divisor.

EXAMPLE 2

Step 1:  Polynomials are already in standard form.

Step 2: x divides into x2 x times.

Step 3: x (x - 3) = x2 - 3x

Step 4: In order to subtract  x2 - 3x from  x2 + 3x, change the signs of  x2 - 3x and it becomes  -x2 + 3x.   This gives us 6x - 18.

2nd time through:

Step 2: x divides into 6x 6 times.

Step 3: 6(x - 3) = 6x - 18

Step 4:  Change the signs of 6x - 18 and get -6x + 18.  This give us a remainder of zero.
 

 

When 2x2 - 5x + 12 is divided by
2x + 1, the result is

  

 

  

Step 1:  Polynomials are already in standard form.

Step 2: 2x divides into 2x2 x times.

Step 3: x (2x + 1) = 2x2 + x

Step 4: In order to subtract  2x2 + x from  2x2 -   5x, change the signs of  2x2 + x and it becomes  -2x2 - x.  This gives us -6x + 12.

2nd time through:

Step 2: 2x divides into -6x    -3 times.

Step 3: -3(2x + 1) = -6x - 3

Step 4:  Change the signs of -6x - 3 and get 6x + 3.  This give us a remainder of 15.