9.7 Dividing Monomials & Polynomials

Front

What is the quotient rule for dividing monomials?

Back

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

Front

Simplify the expression: \( \frac{5x^3y^2}{5xy} \)

Back

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

Front

What is a monomial?

Back

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

Front

What is a polynomial?

Back

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

Front

How do you divide a polynomial by a monomial?

Back

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

Front

Simplify the expression: \( \frac{18y^{6} + 9y^{4} - 12y^{2}}{3y^{2}} \)

Back

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

Front

What is the result of dividing \( -18x^5 - 12x^3 - 6x^2 \) by \( -3x \)?

Back

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

Front

What does it mean to simplify a polynomial?

Back

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

Front

What is a like term in polynomials?

Back

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

Front

What is the degree of a polynomial?

Back

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