To divide a polynomial by a monomial, divide each term of the polynomial by the monomial. To do this, use the quotient rule and divide coefficients and subtract exponents with the same base.

Polynomial division can be modeled with algebra tiles.

Create an area model where:

- The tiles on the inside add up to the dividend (numerator).
- The tiles on one side add up to the divisor (denominator).
- The sum of the tiles along the other side must be the quotient (the result of the division).

Note: Final answers are usually written without any negative exponents.

Simplify the following: \dfrac{3 x^{5} + 4 x^{2}}{x}

Worked Solution

Simplify the following: \dfrac{6 y^{3} - 15 y^{2} + 24y}{3y}

Worked Solution

The triangle shown has an area of 13n^3+11n^2+29n.

Find a simplified polynomial expression for its height.

Worked Solution

Idea summary

When dividing a polynomial by a monomial, we divide each term of the polynomial by the monomial then simplify each individual fraction using the rules of exponents.