Factor and Remainder Theorem

Front

What is the Factor Theorem?

Back

The Factor Theorem states that a polynomial P(x) has a factor (x - c) if and only if P(c) = 0.

Front

What is the Remainder Theorem?

Back

The Remainder Theorem states that when a polynomial P(x) is divided by (x - c), the remainder is P(c).

Front

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

Back

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

Front

How do you find the value of a polynomial at a specific point using synthetic division?

Back

To find f(5) for f(x) = 3x^2 - 9x - 20, use synthetic division with x = 5.

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 result of dividing (2x^3 + 7x^2 - 6x - 8) by (x + 4)?

Back

The result is 2x^2 - x - 2.

Front

What does it mean if a polynomial has a remainder of 0 when divided by (x - c)?

Back

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

Front

What polynomial divided by (x - 2) gives (x^2 - x - 3) with a remainder of -3?

Back

The polynomial is x^3 - 3x^2 - x + 3.

Front

What is the remainder when 2x^3 - 3x^2 + 4x - 5 is divided by (x - 1)?

Back

The remainder is 0.

Front

How do you determine if a polynomial has a root at x = c?

Back

Evaluate the polynomial at c; if P(c) = 0, then x = c is a root.