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 perform Synthetic Division?

Back

Synthetic Division is a simplified form of polynomial long division that uses the coefficients of the polynomial and the root of the divisor.

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

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

Back

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

Front

What is the relationship between roots and factors of a polynomial?

Back

If r is a root of the polynomial P(x), then (x - r) is a factor of P(x).

Front

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

Back

The remainder is 104.

Front

Which polynomial has a remainder of -3 when divided by (x - 2)?

Back

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

Front

What does it mean if a polynomial has a factor?

Back

It means that the polynomial can be expressed as the product of that factor and another polynomial.

Front

How can you determine if (x + 1) is a factor of f(x) = x^3 - 6x^2 + 3x + 10?

Back

Evaluate f(-1). If f(-1) = 0, then (x + 1) is a factor.