Given a quadratic factor, find all the zeros

The video tutorial explains the concept of polynomial factors, focusing on how to determine if a polynomial is a factor of another. It covers the use of division, particularly long division, to verify factors and find zeros. The tutorial also discusses the limitations of synthetic division and demonstrates the process of rewriting polynomials in factored form to identify zeros and achieve linear factorization.

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

• It can be divided by another polynomial to yield the original expression.

• It can be subtracted from the polynomial to get a new expression.

• It can be multiplied by another polynomial to yield the original expression.

• It can be added to the polynomial to get a new expression.

Why is long division preferred over synthetic division in this context?

• Long division is more accurate.

• Long division is faster.

• Synthetic division is more complex.

• Synthetic division is only applicable for linear factors.

What is a common mistake students make during polynomial division?

• Using synthetic division instead of long division.

• Not using the correct divisor.

• Incorrectly adding and subtracting terms.

• Forgetting to multiply terms.

What indicates that a polynomial is a factor of another polynomial during division?

• The quotient is zero.

• The divisor is larger than the dividend.

• The remainder is non-zero.

• The remainder is zero.

How can you find the zeros of a polynomial once it is factored?

• By multiplying all factors together.

• By setting each factor equal to zero.

• By adding all factors together.

• By dividing the polynomial by its factors.

What is the zero product property used for in polynomial factorization?

• To multiply factors to get the original polynomial.

• To add factors to get the original polynomial.

• To find the zeros of the polynomial.

• To divide the polynomial by its factors.

What is the purpose of writing a polynomial in linear factorization?

• To multiply the polynomial by another polynomial.

• To find the zeros of the polynomial.

• To divide the polynomial by another polynomial.

• To simplify the polynomial.