Polynomial Division

Front

What is polynomial division?

Back

Polynomial division is the process of dividing a polynomial by another polynomial of the same or lower degree, similar to long division with numbers.

Front

What is the result of dividing a polynomial by a linear factor?

Back

The result is a polynomial of one degree lower than the original polynomial, plus a remainder.

Front

What is synthetic division?

Back

Synthetic division is a simplified form of polynomial division that is used when dividing by a linear factor of the form (x - c). It is faster and requires less writing.

Front

When should you use long division instead of synthetic division?

Back

Use long division when dividing by a polynomial of degree greater than 1 or when the divisor is not in the form (x - c).

Front

What is the remainder theorem?

Back

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

Front

What is the factor theorem?

Back

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

Front

How do you perform polynomial long division?

Back

1. Divide the leading term of the dividend by the leading term of the divisor. 2. Multiply the entire divisor by this result. 3. Subtract this from the dividend. 4. Repeat the process with the new polynomial.

Front

What is the degree of a polynomial?

Back

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

Front

What is a polynomial?

Back

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

Front

What is the standard form of a polynomial?

Back

The standard form of a polynomial is written in descending order of the degree of its terms.