Remainder Theorem

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 that division is equal to f(c).

Front

How do you find the remainder when dividing a polynomial by a linear divisor?

Back

To find the remainder when dividing a polynomial f(x) by a linear divisor (x - c), evaluate f(c).

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

What is the value of k in the polynomial x^3 - kx^2 + 2x + 5 if the remainder is 2 when divided by x - 3?

Back

The value of k is 4.

Front

How do you evaluate a polynomial function at a specific value?

Back

To evaluate a polynomial function f(x) at a specific value a, substitute a into the polynomial and simplify.

Front

What is the remainder when a^3 - 4 is divided by a + 2?

Back

The remainder is -12.

Front

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

Back

If the remainder is 0, it means that the linear factor is a root of the polynomial.

Front

How can you use the Remainder Theorem to find roots of a polynomial?

Back

By applying the Remainder Theorem, if f(c) = 0 for some value c, then (x - c) is a factor of the polynomial f(x).

Front

What is the significance of the coefficients in synthetic division?

Back

The coefficients in synthetic division represent the coefficients of the polynomial being divided, and they are used to perform the division process.

Front

What is the result of evaluating f(5) for the polynomial f(x) = 5x^2 - 7x - 10?

Back

The result is 80.