Synthetic/Long Division and Polynomial Operations

Front

What is Synthetic Division?

Back

A method used to divide a polynomial by a binomial of the form (x - c) without using long division.

Front

What is Long Division in Polynomials?

Back

A process similar to numerical long division, used to divide polynomials by polynomials.

Front

How do you multiply two binomials?

Back

Use the distributive property (FOIL method) to multiply each term in the first binomial by each term in the second.

Front

What is the result of (5x - 1)(x + 1)?

Back

5x² + 4x - 1.

Front

How do you divide a polynomial by a monomial?

Back

Divide each term of the polynomial by the monomial.

Front

What is the result of dividing 16x⁴ + 8x³ - 4x² by 4x²?

Back

4x² + 2x - 1.

Front

What is the Remainder Theorem?

Back

If a polynomial f(x) is divided by (x - c), the remainder is f(c).

Front

What is the Factor Theorem?

Back

A polynomial f(x) has a factor (x - c) if and only if f(c) = 0.

Front

What is the result of dividing 4x⁴ + 4x³ - 9x² - x + 2 by x - 1?

Back

4x³ + 8x² - x - 2.

Front

What is the standard form of a polynomial?

Back

A polynomial is in standard form when its terms are written in descending order of their degree.