9.7 Dividing Monomials & Polynomials

The quotient rule states that when dividing two monomials, you subtract the exponents of like bases: \( \frac{a^m}{a^n} = a^{m-n} \).

The simplified expression is \( x^2y \).

A monomial is a polynomial with only one term, which can be a number, a variable, or a product of numbers and variables.

A polynomial is an expression that consists of variables raised to non-negative integer powers and coefficients, combined using addition, subtraction, and multiplication.

To divide a polynomial by a monomial, divide each term of the polynomial by the monomial separately.

The simplified expression is \( 6y^{4} + 3y^{2} - 4 \).

The result is \( 6x^4 + 4x^2 + 2x \).

Simplifying a polynomial means to combine like terms and reduce the expression to its simplest form.

Like terms are terms that have the same variable raised to the same power, allowing them to be combined.

The degree of a polynomial is the highest power of the variable in the expression.