Direct, long, and synthetic division

Front

What is synthetic division?

Back

A method for dividing a polynomial by a linear divisor, simplifying the process by using coefficients.

Front

How do you set up synthetic division?

Back

Write the coefficients of the polynomial in descending order, and use the zero of the divisor as the number to the left.

Front

What is the purpose of using placeholders in synthetic division?

Back

Placeholders are used for missing degrees of terms to maintain the correct alignment of coefficients.

Front

What is the remainder theorem?

Back

If a polynomial f(x) is divided by (x - c), the remainder is f(c).

Front

How do you find the remainder when dividing a polynomial?

Back

Evaluate the polynomial at the value of the zero of the divisor.

Front

What is the difference between long division and synthetic division?

Back

Long division is a more general method applicable to any polynomial division, while synthetic division is a shortcut for linear divisors.

Front

What is the significance of the leading coefficient in polynomial division?

Back

The leading coefficient affects the degree and the end behavior of the polynomial.

Front

How do you determine the order of coefficients in polynomial division?

Back

The order is determined by the descending powers of x, starting from the highest degree.

Front

What happens if you forget to include a zero placeholder in synthetic division?

Back

It can lead to incorrect calculations and an inaccurate remainder.

Front

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

Back

The remainder is 5.