Dividing Polynomials by Monomials

Front

What is a polynomial?

Back

A polynomial is a mathematical expression that consists of variables, coefficients, and non-negative integer exponents, combined using addition, subtraction, and multiplication.

Front

What is a monomial?

Back

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

Front

What does it mean to divide a polynomial by a monomial?

Back

Dividing a polynomial by a monomial involves simplifying each term of the polynomial by the monomial, reducing the degree of the variables.

Front

How do you simplify the expression (45x^6y^9) / (5x^4y^2)?

Back

The simplified expression is 9x^2y^7.

Front

What is the quotient rule in polynomial division?

Back

Front

How do you divide the polynomial 8x^2 - 4x + 12 by 2x?

Back

The result is 4x - 2 + 6/x.

Front

Back

The result is 2x^4 - 3x^2 + 1.

Front

What happens to the exponents when dividing like terms?

Back

When dividing like terms, you subtract the exponent of the denominator from the exponent of the numerator.

Front

What is the simplified form of 15x^9 - 8x^3 divided by 3x^6?

Back

The simplified form is 5x^3 - rac{8}{3}.

Front

What is the first step in dividing polynomials by monomials?

Back

The first step is to divide each term of the polynomial by the monomial separately.