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 distributing the division across each term of the polynomial and simplifying the resulting expression.

Front

What is the quotient rule for exponents?

Back

The quotient rule states that when dividing two powers with the same base, you subtract the exponents: a^m / a^n = a^(m-n).

Front

Simplify: (x^5)/(x^2)

Back

x^(5-2) = x^3.

Front

How do you simplify the expression (12x^4 + 8x^3) / 4x^2?

Back

Divide each term by 4x^2: (12x^4)/4x^2 + (8x^3)/4x^2 = 3x^2 + 2x.

Front

What is the result of dividing 45x^6y^9 by 5x^4y^2?

Back

(45/5)(x^(6-4))(y^(9-2)) = 9x^2y^7.

Front

Divide: 8x^2 - 4x + 12 by 2x

Back

(8x^2)/2x - (4x)/2x + (12)/2x = 4x - 2 + 6/x.

Front

What is the result of (9x^2 + 6x) ÷ 3x?

Back

(9x^2)/3x + (6x)/3x = 3x + 2.

Front

What is the first step in dividing polynomials by monomials?

Back

Identify the leading term of the polynomial and divide it by the monomial.