Synthetic Division

Front

What is synthetic division?

Back

A method used to divide a polynomial by a linear divisor 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 and the zero of the divisor.

Front

How do you handle missing exponents in synthetic division?

Back

You must put a zero as a coefficient placeholder for any missing exponent.

Front

What does the left-hand box represent in synthetic division?

Back

It represents the zero of the divisor (x - c), where c is the value that makes the divisor equal to zero.

Front

What is the result of (3x^3 + 5x - 1) ÷ (x + 1)?

Back

3x^2 - 3x + 8 - 9/(x + 1).

Front

What is the result of (2x^3 - 5x - 7) ÷ (x - 2)?

Back

2x^2 + 4x + 3 - 1/(x - 2).

Front

In synthetic division, what do you do after bringing down the first coefficient?

Back

Multiply the number in the left-hand box by the number just brought down.

Front

What is the purpose of synthetic division?

Back

To simplify the process of dividing polynomials, especially when the divisor is a linear polynomial.

Front

What is the relationship between synthetic division and polynomial long division?

Back

Synthetic division is a simplified form of polynomial long division that is faster and easier for linear divisors.

Front

What do you do with the remainders in synthetic division?

Back

The remainder is expressed as a fraction over the divisor.