Remainder Theorem 10.11.24

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 equal to f(c).

Front

How do you evaluate a polynomial at a specific point?

Back

To evaluate a polynomial p(x) at a point x = a, substitute a into the polynomial and simplify.

Front

What is synthetic division?

Back

Synthetic division is a simplified form of polynomial long division that is used specifically for dividing by linear factors of the form (x - c).

Front

If p(x) = x^3 - 5x^2 + 2x - 10, what is p(5)?

Back

0

Front

Given P(x) = x^3 + x^2 - x - 9, what is P(4)?

Back

67

Front

How do you find the remainder of a polynomial division?

Back

To find the remainder of a polynomial f(x) divided by (x - c), evaluate f(c).

Front

What is the result of dividing (10x^4 - 50x^3 - 800) by (x - 6)?

Back

1,360

Front

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

Back

-113

Front

If f(x) = x^4 + 5x^3 - 19x^2 - 23x, how do you find f(-5) using synthetic division?

Back

The value of f(-5) is -360.

Front

What is the significance of the remainder in polynomial division?

Back

The remainder gives information about the polynomial's value at specific points and can indicate whether (x - c) is a factor of the polynomial.