PreCalculus Flashcard 2.3

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 and requires less writing than long division.

Front

What is the first step in synthetic division?

Back

The first step is to write down the coefficients of the polynomial in descending order of degree.

Front

In synthetic division, what do you do with the first coefficient?

Back

You bring down the first coefficient unchanged.

Front

What do you do after bringing down the first coefficient in synthetic division?

Back

Multiply the first coefficient by the value of c (from x - c) and write the result under the next coefficient.

Front

What is the purpose of adding the numbers in synthetic division?

Back

Adding the numbers helps to find the new coefficients of the quotient polynomial.

Front

What does the remainder represent in synthetic division?

Back

The remainder represents the value of the original polynomial evaluated at x = c.

Front

How do you determine the degree of the quotient in synthetic division?

Back

The degree of the quotient is one less than the degree of the original polynomial.

Front

What is the significance of the number 'c' in synthetic division?

Back

The number 'c' is the root of the divisor (x - c) and is the value at which the polynomial is evaluated.

Front

What is the result of synthetic division if the remainder is zero?

Back

If the remainder is zero, it means that (x - c) is a factor of the polynomial.

Front

What is the next step after completing synthetic division?

Back

The next step is to write the quotient polynomial and the remainder in the form: quotient + (remainder)/(divisor).