Synthetic Division of Polynomials

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 write down the coefficients of the polynomial in descending order of degree, filling in any missing degrees with zeros.

Front

How do you set up synthetic division for (2x^3 + 5x^2 + 9) ÷ (x + 3)?

Back

Use -3 (the root of x + 3) and the coefficients: 2, 5, 0, 9.

Front

What do you do with the first coefficient in synthetic division?

Back

Bring down the first coefficient unchanged to the bottom row.

Front

What is the process after bringing down the first coefficient in synthetic division?

Back

Multiply the number you just brought down by the root (c) and add it to the next coefficient.

Front

What does the last number in synthetic division represent?

Back

The last number represents the remainder of the division.

Front

How do you write the final answer after synthetic division?

Back

The final answer is written as the quotient polynomial plus the remainder over the divisor.

Front

What is the quotient when dividing (2x^3 + 5x^2 + 9) by (x + 3)?

Back

The quotient is 2x^2 - x + 3.

Front

What is the importance of the order of coefficients in synthetic division?

Back

The order of coefficients must match the descending powers of x to ensure accurate calculations.

Front

How many zeros do you need for the polynomial x^6 + 4x^3 + 2 in synthetic division?

Back

You need 4 zeros for the missing degrees (x^5, x^4, x^2, x^1).