Diving Polynomials with Synthetic Division Flashcard

Front

What is synthetic division?

Back

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

Front

What is the first step in synthetic division?

Back

The first step is to set up the synthetic division by writing the coefficients of the polynomial and the value of c from the divisor (x - c).

Front

How do you find the quotient in synthetic division?

Back

To find the quotient, you perform synthetic division by bringing down the leading coefficient and multiplying it by c, then adding it to the next coefficient, and repeating this process.

Front

What is the remainder in synthetic division?

Back

The remainder is the last number obtained after completing the synthetic division process. It represents the leftover part of the polynomial after division.

Front

What is the relationship between the degree of the dividend and the degree of the quotient?

Back

The degree of the quotient is always one less than the degree of the dividend when dividing by a linear polynomial.

Front

If a polynomial f(x) is divided by (x - c), what does f(c) represent?

Back

f(c) represents the remainder of the division of f(x) by (x - c). If f(c) = 0, then (x - c) is a factor of f(x).

Front

What is the quotient when 4x^3 - 9x^2 + 5x - 2 is divided by x - 2?

Back

4x^2 + x + 3

Front

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

Back

2x - 1

Front

Determine the quotient when 3x^2 - 11x + 6 is divided by x - 2.

Back

3x - 5

Front

When x^2 - 4x + 4 is divided by x - 2, what is the quotient?

Back

x - 2