How to Find Remaining Factors of a Polynomial Using Synthetic Division - Polynomial

The video tutorial explains how to determine if a given expression is a factor of a polynomial using synthetic division. It emphasizes the importance of finding all remaining factors by breaking down the polynomial into linear factors. The process of synthetic division is demonstrated, showing how it can prove a factor by resulting in a remainder of zero. The tutorial also highlights the difference between simply plugging in values and using synthetic division for a comprehensive factorization.

What does it mean for an expression to be a factor of a polynomial?

• It divides the polynomial with a remainder.

• It divides the polynomial without a remainder.

• It is a multiple of the polynomial.

• It is equal to the polynomial.

Why is synthetic division preferred over simply plugging in values to check for factors?

• It does not require any calculations.

• It is the only method to find factors.

• It provides the quotient, which helps in further factorization.

• It is faster and more accurate.

What is the result of synthetic division if the expression is a factor?

• A non-zero remainder

• A zero remainder

• A negative remainder

• An undefined remainder

What is the next step after confirming a factor using synthetic division?

• Find the derivative

• Stop the process

• Multiply the quotient

• Factor the quotient further

Which of the following is a linear factor of the polynomial X^2 + X - 2?

• X + 2

• X - 2

• X - 1

• X + 3