Synthetic and Long division

Front

What is synthetic division?

Back

Synthetic division is a simplified method of dividing a polynomial by a linear binomial of the form (x - c). It is faster than long division and is used when the divisor is a linear polynomial.

Front

What is the remainder theorem?

Back

The remainder theorem states that the remainder of the division of a polynomial p(x) by (x - c) is equal to p(c).

Front

How do you find the remainder of a polynomial when divided by a linear binomial?

Back

To find the remainder of a polynomial p(x) when divided by (x - c), substitute c into the polynomial p(c).

Front

What is long division in polynomials?

Back

Long division in polynomials is a method used to divide a polynomial by another polynomial, similar to numerical long division, where you divide, multiply, and subtract repeatedly.

Front

What is the first step in synthetic division?

Back

The first step in synthetic division is to write down the coefficients of the polynomial being divided.

Front

What is the purpose of synthetic division?

Back

The purpose of synthetic division is to simplify the process of dividing polynomials, especially when the divisor is a linear polynomial.

Front

What is the result of dividing (4x^3 - 3x^2 - 4x + 2) by (x - 3)?

Back

The result is 4x^2 + 9x + 23 with a remainder of 71.

Front

What is the result of dividing (2x^3 - 5x^2 + 3x + 7) by (x - 2)?

Back

The result is 2x^2 - x + 1 with a remainder of 9.

Front

What is the remainder when (x^3 - 5x^2 - 8x + 1) is divided by (x + 1)?

Back

The remainder is 3.

Front

What is the remainder when p(x) = x^3 - 5x^2 + 2x - 10 is divided by (x - 5)?

Back

The remainder is 0.