Remainder and Factor Theorem - Flashcard 2

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 that division 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 determine if a binomial is a factor of a polynomial?

Back

To determine if (x - c) is a factor of f(x), evaluate f(c). If f(c) = 0, then (x - c) is a factor.

Front

Evaluate P(2) for P(x) = 2x^4 + x^3 - 3x^2 - x - 15.

Back

P(2) = 11.

Front

Evaluate P(3) for P(x) = 3x^3 + 5x^2 - 4x - 8.

Back

P(3) = 106.

Front

What is the value of P(2) for P(x) = 9x^4 - 45x^3 + 37x^2 + x + 2?

Back

P(2) = -64.

Front

If f(x) = x^3 - 6x^2 + 3x + 10, which binomial is a factor?

Back

x + 1.

Front

If f(x) = x^3 + x^2 - 24x + 36, which binomial is a factor?

Back

x + 6.

Front

What is the significance of evaluating a polynomial at a specific point?

Back

Evaluating a polynomial at a specific point helps determine the remainder when divided by a linear factor.

Front

What is synthetic division?

Back

Synthetic division is a simplified method of dividing a polynomial by a binomial of the form (x - c).