Dividing Polynomials (Long Division)

Dividing Polynomials (Long Division)

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

Example 1

Simplify the given expression. (a^2 - 7a + 10)/a

See the meaning of each part.

Quotient: a - 7
Remainder: 10
Divisor: a

Example 2

Simplify the given expression. (x^3 - 7x + 11)/(x - 2)

Write the numerator and the denominator
as a division of natural numbers.

Don't forget to make a space for x2 term.

To remove x3,
write x2 on the quotient part
and write x3 - 2x2. [= x2(x - 2)]

After subtraction, 2x2 remains.
(x3) - (x3 - 2x2) = 2x2

Write -7x behind 2x2.

To remove 2x2,
write +2x on the quotient part
and write 2x2 - 4x. [= 2x(x - 2)]

After subtraction, -3x remains.
(2x2 - 7x) - (2x2 - 4x) = -3x

Write +11 behind -3x.

To remove -3x,
write -3 on the quotient part
and write -3x + 6. [= -3(x - 2)]

After subtraction, 5 remains.
(-3x + 11) - (-3x + 6) = 5

So the answer is x2 + 2x - 3 + 5/(x - 2).

Quotient: x2 + 2x - 3
Remainder: 5
Divisor: (x - 2)