How to the Remaining Factors When Given One Factor of a Polynomial

The video tutorial explains how to determine if a polynomial has a factor by using synthetic division, ensuring a remainder of zero. It demonstrates the process of synthetic division with an example and emphasizes the importance of rewriting polynomials as linear factors. The tutorial highlights the need for practice in factoring to achieve this goal.

What is the condition for a polynomial to have a factor?

• The factor must divide the polynomial with a remainder of zero.

• The factor must be a linear expression.

• The factor must be a constant.

• The factor must be a quadratic expression.

What is the first step in using synthetic division to find remaining factors?

• Multiply the polynomial by the factor.

• Use the opposite sign of the factor's root.

• Add the factor to the polynomial.

• Subtract the factor from the polynomial.

In synthetic division, what does a remainder of zero indicate?

• The factor divides the polynomial completely.

• The division process needs to be repeated.

• The factor is incorrect.

• The polynomial is not factorable.

Why is it important to express a polynomial in terms of linear factors?

• To make the polynomial easier to graph.

• To simplify the polynomial.

• To fully factor the polynomial into its simplest form.

• To ensure the polynomial is quadratic.

What should be done if a polynomial is not fully expressed in linear factors?

• Leave it as is.

• Multiply it by another polynomial.

• Factor it further to achieve linear factors.

• Convert it to a quadratic form.