Factor and Remainder Theorem

Front

What is the Factor Theorem?

Back

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

Front

What is the Remainder Theorem?

Back

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

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 remainder of a polynomial when divided by (x - r)?

Back

Evaluate the polynomial at r, i.e., find P(r).

Front

What is synthetic division?

Back

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

Front

If the remainder of a polynomial is 0, what does that imply about its factors?

Back

It implies that (x - r) is a factor of the polynomial.

Front

What is the value of p(2) if p(x) = 9x^4 - 45x^3 + 37x^2 + x + 2?

Back

p(2) = -64.

Front

What is the result of dividing x^3 - 3x^2 - x + 3 by (x - 2)?

Back

The quotient is (x^2 - x - 1) with a remainder of -3.

Front

What does it mean if a polynomial has a root at x = r?

Back

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

Front

How can you determine if (x - r) is a factor of P(x)?

Back

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