Synthetic Division

Front

What is synthetic division?

Back

A method for dividing a polynomial by a linear binomial of the form (x - c) without using long division.

Front

What is the first step in synthetic division?

Back

Write down the coefficients of the polynomial in descending order of degree.

Front

How do you determine the number to use in synthetic division?

Back

Use the value of c from the binomial (x - c) as the number in the left-hand box.

Front

What is the purpose of the synthetic division process?

Back

To simplify the division of polynomials and find the quotient and remainder.

Front

If dividing (2x^3 + 5x^2 + 9) by (x + 3), what is the result?

Back

2x^2 - x + 3.

Front

In synthetic division, what do you do with the number in the left-hand box?

Back

Multiply it by the current value in the bottom row and add it to the next coefficient.

Front

What does the remainder represent in synthetic division?

Back

The value left over after dividing the polynomial, which can be expressed as a fraction over the divisor.

Front

How many zeros are needed in synthetic division for the polynomial x^6 + 4x^3 + 2?

Back

4 zeros.

Front

What is the order of coefficients for the polynomial (3x - 4x^3 + 6x^4 + 1) when dividing by (x + 3)?

Back

6, -4, 0, 3, 1.

Front

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

Back

It determines the leading term of the quotient polynomial.