Remainder theorem/Factor theorem

Front

What is the Remainder Theorem?

Back

The Remainder Theorem states that if a polynomial f(x) is divided by (x - c), the remainder of this division is 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

Calculate f(5) for f(x) = 3x² - 9x - 20.

Back

f(5) = 10.

Front

What is the remainder when a³ - 4 is divided by a + 2?

Back

The remainder is -12.

Front

Is (x - 7) a factor of (x² - 5x + 14)?

Back

No, (x - 7) is not a factor.

Front

What is synthetic division?

Back

Synthetic division is a simplified form of polynomial long division that is used when dividing by a linear factor.

Front

What is the result of (2x³ - 5x² + 3x + 7) ÷ (x - 2)?

Back

The result is 2x² - x + 1 + 9/(x - 2).

Front

Define polynomial long division.

Back

Polynomial long division is a method for dividing a polynomial by another polynomial of equal or lower degree.

Front

What does it mean for a polynomial to be a factor of another polynomial?

Back

A polynomial f(x) is a factor of g(x) if g(x) can be expressed as g(x) = f(x) * q(x) for some polynomial q(x).

Front

What is the significance of the remainder in polynomial division?

Back

The remainder provides information about the value of the polynomial at specific points and can indicate factors.