Synthetic and Long division

Front

What is synthetic division?

Back

A method for dividing a polynomial by a linear binomial of the form (x - c) using coefficients.

Front

What is the purpose of using a zero placeholder in synthetic division?

Back

To ensure that all terms of the polynomial are accounted for, especially when a term is missing.

Front

How do you find the remainder when dividing a polynomial by (x - c)?

Back

Evaluate the polynomial at x = c using the Remainder Theorem.

Front

What is the Remainder Theorem?

Back

It states that the remainder of the division of a polynomial p(x) by (x - c) is p(c).

Front

What is the first step in synthetic division?

Back

Write down the coefficients of the polynomial in descending order.

Front

When dividing (2x³ + 4x² - 5) by (x + 3), what is the first coefficient used in synthetic division?

Back

2, which is the coefficient of x³.

Front

What mistake did Cam make when dividing (x⁴ + 3x² - 4x - 2) by (x - 2)?

Back

He did not use a zero placeholder for the x³ term.

Front

What is the result of dividing (4x³ - 3x² - 4x + 2) by (x - 3)?

Back

The remainder is 71.

Front

What is the remainder when p(x) = x³ - 5x² + 2x - 10 is divided by (x - 5)?

Back

The remainder is 0.

Front

What is the result of (2x³ + 5x² + 9) ÷ (x + 3)?

Back

The result is 2x² - x + 3.