dividing polynomials by monomials

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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. Example: 3x^2 + 2x - 5.

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What is a monomial?

Back

A monomial is a polynomial with only one term. It can be a constant, a variable, or a product of constants and variables. Example: 4x^3.

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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. Example: (6x^2 + 12x) / 3x = 2x + 4.

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What is the quotient in polynomial division?

Back

The quotient is the result obtained when one polynomial is divided by another polynomial. It represents how many times the divisor fits into the dividend.

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What is the remainder in polynomial division?

Back

The remainder is what is left over after dividing one polynomial by another. It can be expressed as a polynomial of lower degree than the divisor.

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What is the degree of a polynomial?

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The degree of a polynomial is the highest power of the variable in the polynomial. Example: The degree of 4x^3 + 2x^2 - 5 is 3.

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What does it mean to simplify an expression?

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To simplify an expression means to reduce it to its simplest form by combining like terms and eliminating any unnecessary parts.

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What is a like term?

Back

Like terms are terms in a polynomial that have the same variable raised to the same power. Example: 3x^2 and 5x^2 are like terms.

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How do you factor a polynomial?

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Factoring a polynomial involves expressing it as a product of its factors. Example: x^2 - 9 can be factored as (x - 3)(x + 3).

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What is the area of a rectangle?

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The area of a rectangle is calculated by multiplying its length by its width. Example: Area = length × width.