Question
Under which condition can synthetic division be used instead of long division for polynomials?
(10 points)
When dividing any polynomial by any other polynomial.
When dividing by a linear polynomial (degree of 1) with a leading coefficient of 1.
When dividing by a polynomial of any degree.
When dividing by a quadratic (degree of 2) polynomial.
(10 points)
When dividing any polynomial by any other polynomial.
When dividing by a linear polynomial (degree of 1) with a leading coefficient of 1.
When dividing by a polynomial of any degree.
When dividing by a quadratic (degree of 2) polynomial.
Answers
GPT-5 mini
When dividing by a linear polynomial (degree of 1) with a leading coefficient of 1.
Reason: Synthetic division is a shortcut for dividing by divisors of the form x − c (leading coefficient 1). It uses the root c in a compact tabular process; it does not apply directly to higher-degree divisors.
Reason: Synthetic division is a shortcut for dividing by divisors of the form x − c (leading coefficient 1). It uses the root c in a compact tabular process; it does not apply directly to higher-degree divisors.