How division relate to linear factorization and zeros

The video tutorial explains how to find the zeros of a polynomial using long division. It begins with an introduction to the concept, followed by a detailed step-by-step demonstration of long division on polynomials. The tutorial then discusses the significance of remainders in polynomial division and how to factor polynomials to find their zeros. The video concludes with a summary of the process and final thoughts on the topic.

What is the first step in using long division to find the zeros of a polynomial?

• Add the divisor to the dividend

• Divide the leading term of the dividend by the leading term of the divisor

• Subtract the divisor from the dividend

• Multiply the divisor by the dividend

What does a zero remainder indicate when dividing polynomials?

• The division process is incorrect

• The dividend is a prime polynomial

• The divisor is not a factor of the dividend

• The divisor is a factor of the dividend

How can a polynomial be rewritten if it divides evenly by another polynomial?

• As a quotient of its factors

• As a sum of its factors

• As a product of its factors

• As a difference of its factors

What is the purpose of factoring a polynomial further after rewriting it in factored form?

• To simplify the polynomial

• To find the zeros of the polynomial

• To increase the degree of the polynomial

• To change the polynomial's coefficients

What are the zeros of the polynomial X^3 - X^2 - 9X + 9?

• 1/3 and -3

• 3 and -1/3

• 1 and -3

• 9 and -1