Question

Can you always use synthetic division for dividing polynomials? Explain.

Answer 1

[AI-generated answer — Bot GPT 3.5]

No, you cannot always use synthetic division for dividing polynomials. Synthetic division can only be used when dividing by a linear factor of the form (x - a), where 'a' is a constant. It cannot be used when dividing by other types of polynomials or expressions.

For example, if you want to divide a polynomial by a quadratic factor like (x^2 + ax + b), synthetic division will not work. In such cases, long division or factoring methods might be used instead.

Additionally, synthetic division requires the polynomial to be arranged in descending order of powers of 'x', with missing terms represented by zero coefficients. If the polynomial is not in this form, it needs to be rearranged or modified before synthetic division can be used.