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 this 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 a binomial (x - c) is a factor of a polynomial f(x), evaluate f(c). If f(c) = 0, then (x - c) is a factor.

Front

What is the value of P(3) for the polynomial P(x) = 3x^3 + 5x^2 - 4x - 8?

Back

P(3) = 106.

Front

What is the value of P(2) for the polynomial P(x) = 2x^4 + x^3 - 3x^2 - x - 15?

Back

P(2) = 11.

Front

What is synthetic division?

Back

Synthetic division is a simplified form of polynomial long division that is used specifically for dividing by linear factors of the form (x - c).

Front

How do you find the remainder when dividing a polynomial by a binomial?

Back

You can find the remainder by evaluating the polynomial at the value that makes the binomial zero, using the Remainder Theorem.

Front

What is the significance of the coefficients in a polynomial?

Back

The coefficients of a polynomial determine the shape and position of the graph of the polynomial function.

Front

What is the degree of the polynomial f(x) = x^3 - 6x^2 + 3x + 10?

Back

The degree of the polynomial is 3, which is the highest power of x in the polynomial.

Front

What does it mean for a polynomial to be factored completely?

Back

A polynomial is factored completely when it is expressed as a product of irreducible polynomials over the given number system.