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 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

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

Back

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

Front

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

Back

P(2) = 11.

Front

What is the remainder when dividing 2x^3 - 2x^2 + x + 4 by x - 4?

Back

The remainder is 104.

Front

Which binomial is a factor of f(x) = x^3 + x^2 - 24x + 36?

Back

x + 6 is a factor.

Front

Which binomial is a factor of f(x) = x^3 - 6x^2 + 3x + 10?

Back

x + 1 is a factor.

Front

How do you determine if a polynomial has a factor?

Back

Evaluate the polynomial at the root; if the result is zero, then the corresponding binomial is a factor.

Front

What is synthetic division?

Back

Synthetic division is a simplified form of polynomial long division used to divide a polynomial by a linear factor.

Front

What is the significance of the coefficients in polynomial division?

Back

The coefficients determine the terms of the polynomial and affect the degree and behavior of the polynomial.