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

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

Back

You can find the remainder by evaluating the polynomial at the value of c in the binomial (x - c).

Front

If P(-4) = 0, what can be concluded about P(x)?

Back

x + 4 is a factor of P(x).

Front

What is a factor of a polynomial?

Back

A factor of a polynomial is a polynomial that divides the original polynomial without leaving a remainder.

Front

Given P(x) = 9x^4 - 45x^3 + 37x^2 + x + 2, what is P(2)?

Back

P(2) = -64.

Front

What does it mean if P(c) = 0 for a polynomial P(x)?

Back

It means that (x - c) is a factor of P(x) and c is a root of the polynomial.

Front

How do you determine if a binomial is a factor of a polynomial?

Back

You can use synthetic division or the Remainder Theorem to check if the remainder is zero when dividing the polynomial by the binomial.

Front

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

Back

P(2) = 11.

Front

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

Back

x + 1 is a factor.

Front

What is the significance of the Factor Theorem?

Back

The Factor Theorem provides a way to determine if a polynomial has a specific linear factor based on its roots.