When Given a Factor Find the Remaining Zeros of Polynomial

The video tutorial explains how to find the zeros of a polynomial using factors and division methods. It begins with an introduction to factoring and non-factorable equations, followed by a detailed explanation of factors and their role in finding zeros. The tutorial then covers the synthetic division process, providing step-by-step instructions. Finally, it demonstrates solving for zeros using both factoring and division techniques.

What does a factor tell us about a polynomial?

• It multiplies the polynomial to increase its degree.

• It is a number that can be added to the polynomial.

• It divides the polynomial without a remainder.

• It is a number that can be subtracted from the polynomial.

Why is synthetic division preferred over long division for certain polynomials?

• It provides more accurate results.

• It is easier and can be used when the divisor is a linear binomial.

• It is faster and can be used for any polynomial.

• It can be used for polynomials with any degree.

What is the first step in synthetic division?

• Add the coefficients of the polynomial.

• Find the zero of the factor.

• Subtract the divisor from the polynomial.

• Multiply the polynomial by the divisor.

In synthetic division, what do you do after bringing down the first term?

• Add all the terms together.

• Multiply on the diagonals and add on the vertical.

• Divide the terms by the factor.

• Subtract the factor from each term.

What does a remainder of 0 indicate in synthetic division?

• The divisor is not a factor of the polynomial.

• The polynomial is not divisible by the divisor.

• The divisor evenly divides the polynomial.

• The polynomial has no zeros.

How do you find the zeros of a polynomial after factoring?

• Set each factor equal to zero.

• Multiply the factors together.

• Divide the factors by the polynomial.

• Add the factors together.

What are the zeros of the polynomial in the example provided?

• 3, -1, and -5

• 2, -3, and 5

• 1, -2, and 4

• 0, -1, and 3