Question

When can you only use synthetic division?

1) When dividing by a polynomial
2) When dividing by a rational number
3) When dividing by a whole number
4) When dividing by a complex number

Answer 1

Synthetic division is specifically used when dividing by a polynomial of the form (x - c). It is not applicable for divisions involving a rational number, whole number, or complex number. Simplifying and checking the result are essential for accurate division.

Step-by-step explanation:

Synthetic division can be used only when dividing by a polynomial of the form (x - c), where c is a constant.

This is particularly helpful when the polynomial being divided is a monic linear polynomial, or more simply, has a leading coefficient of 1.

It cannot be used when dividing by a rational number, a whole number, or a complex number as these types of division do not meet the criteria for synthetic division.

It's important to simplify the algebra by eliminating terms wherever possible and to check the answer to confirm its reasonableness.

These steps ensure that the division process is carried out correctly and the final result is accurate.