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 this division is equal to f(c).

Front

How can you find the remainder when dividing a polynomial by a linear factor?

Back

Evaluate the polynomial at the value of c, where c is the root of the linear factor (x - c).

Front

What is the remainder when 3x³ - 10x² + 13x - 6 is divided by x - 2?

Back

4

Front

What is the remainder when a³ - 4 is divided by a + 2?

Back

-12

Front

What is the remainder of (3x³ - 5x² - 4x + 1) ÷ (x + 3)?

Back

-113

Front

If -2x³ - 6x² + 5x - 7 is divided by x - 7, what is the correct equation representing this division?

Back

-2x³ - 6x² + 5x - 7 = (x - 7)(-x² - 20x - 135) - 952

Front

When p(x) = 9x⁴ - 45x³ + 37x² + x + 2 is divided by x - 2, how do you find the remainder?

Back

Evaluate p(2).

Front

What is the value of p(2) for the polynomial p(x) = 9x⁴ - 45x³ + 37x² + x + 2?

Back

-64

Front

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

Back

It means that the linear factor is a root of the polynomial.

Front

What is synthetic division and how is it related to the Remainder Theorem?

Back

Synthetic division is a simplified method of dividing polynomials that can be used to find the remainder quickly, confirming the Remainder Theorem.