The video tutorial explains how to use synthetic division to verify if a binomial is a factor of a polynomial. It demonstrates the process step-by-step, showing that if the remainder is zero, the binomial is a factor. The tutorial further explores finding all factors of a polynomial by breaking it down into simpler components. The importance of verifying results through factorization is emphasized, ensuring the original equation is obtained.

What is the condition for a binomial to be considered a factor of a polynomial?

• The remainder is non-zero.

• The remainder is zero.

• The quotient is zero.

• The quotient is non-zero.

In synthetic division, what is the first step after writing down the coefficients?

• Bring down the first coefficient.

• Multiply the divisor by the first coefficient.

• Subtract the divisor from the first coefficient.

• Add the divisor to the first coefficient.

What does a remainder of zero indicate in synthetic division?

• The divisor is not a factor.

• The divisor is a factor.

• The polynomial is quadratic.

• The polynomial is prime.

How can you express a polynomial after finding one of its factors?

• As a product of its factors.

• As a difference of its factors.

• As a quotient of its factors.

• As a sum of its factors.

What is the next step after determining one factor of a polynomial?

• Stop the process.

• Find the derivative.

• Factor the remaining polynomial.

• Integrate the polynomial.