Dividing Polynomials

Front

What is a polynomial?

Back

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

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What does it mean to divide polynomials?

Back

Dividing polynomials involves finding how many times a polynomial (the dividend) can be divided by another polynomial (the divisor), resulting in a quotient and possibly a remainder.

Front

What is the degree of a polynomial?

Back

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

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

What is synthetic division?

Back

Synthetic division is a simplified method of dividing a polynomial by a linear binomial, typically used when the divisor is in the form (x - c).

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What is the remainder theorem?

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The remainder theorem states that the remainder of the division of a polynomial f(x) by (x - c) is equal to f(c).

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What is the factor theorem?

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The factor theorem states that (x - c) is a factor of the polynomial f(x) if and only if f(c) = 0.

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How do you factor a quadratic polynomial?

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To factor a quadratic polynomial of the form ax^2 + bx + c, find two numbers that multiply to ac and add to b, then rewrite the polynomial using these numbers.

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What is long division of polynomials?

Back

Long division of polynomials is a method similar to long division with numbers, used to divide a polynomial by another polynomial.

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.