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

How do you determine if (x - c) is a factor of P(x)?

Back

Evaluate P(c). If P(c) = 0, then (x - c) is a factor of P(x).

Front

What is synthetic division?

Back

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

Front

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

Back

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

Front

Back

The remainder is -2.

Front

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

Back

Perform synthetic division with the divisor (x - c) and evaluate the remainder.

Front

What does it mean if the remainder is 0 when dividing a polynomial?

Back

It means that the divisor is a factor of the polynomial.

Front

What is the first step in synthetic division?

Back

Write down the coefficients of the polynomial.

Front

In synthetic division, what do you do with the number in the left box?

Back

It represents the value of the divisor (c) in (x - c).