# Dividing Polynomials (Long Division)

How to solve dividing polynomial problems by using the long division: examples and their solutions.

## Example 1

See the meaning of each part.

Quotient: *a* - 7

Remainder: 10

Divisor: *a*

## Example 2

Write the numerator and the denominator

as a division of natural numbers.

Don't forget to make a space for *x*^{2} term.

To remove *x*^{3},

write *x*^{2} on the quotient part

and write *x*^{3} - 2*x*^{2}. [= *x*^{2}(*x* - 2)]

After subtraction, 2*x*^{2} remains.

(*x*^{3}) - (*x*^{3} - 2*x*^{2}) = 2*x*^{2}

Write -7*x* behind 2*x*^{2}.

To remove 2*x*^{2},

write +2*x* on the quotient part

and write 2*x*^{2} - 4*x*. [= 2*x*(*x* - 2)]

After subtraction, -3*x* remains.

(2*x*^{2} - 7*x*) - (2*x*^{2} - 4*x*) = -3*x*

Write +11 behind -3*x*.

To remove -3*x*,

write -3 on the quotient part

and write -3*x* + 6. [= -3(*x* - 2)]

After subtraction, 5 remains.

(-3*x* + 11) - (-3*x* + 6) = 5

So the answer is *x*^{2} + 2*x* - 3 + 5/(*x* - 2).

Quotient: *x*^{2} + 2*x* - 3

Remainder: 5

Divisor: (*x* - 2)