Polynomial Division and Factors

The video tutorial explains how to rewrite a polynomial as a product of linear factors, given a known factor. It starts by dividing the polynomial by the known factor, x plus 6, and then proceeds to factor the resulting quadratic expression. The process involves careful organization of terms and understanding of polynomial division and factoring techniques.

What is the known factor of the polynomial p(x) given in the problem?

• x + 6

• x - 6

• x + 3

• x - 3

What is the significance of the factor x + 6 in the polynomial?

• It is a root of the polynomial

• It increases the degree of the polynomial

• It changes the polynomial's sign

• It is a divisor of the polynomial

What is the first step in dividing the polynomial by x + 6?

• Subtracting the constant term

• Aligning terms by degree

• Adding zero terms

• Multiplying by x

Why is it important to include a zero term for missing degrees in polynomial division?

• To make the division faster

• To simplify calculations

• To avoid confusion in alignment

• To increase the degree of the polynomial

Which of the following is a step in the polynomial division process?

• Multiplying by zero

• Dividing by the constant

• Adding terms

• Subtracting the product

What is the result of dividing x^3 + 9x^2 - 108 by x + 6?

• x^2 - 3x + 18

• x^2 + 3x - 18

• x^2 - 6x + 18

• x^2 + 6x - 18

What is the degree of the polynomial after dividing by x + 6?

• 1

• 2

• 3

• 0

What are the two numbers that add up to 3 and multiply to -18 in the quadratic x^2 + 3x - 18?

• 6 and -3

• 5 and -3

• 4 and -4

• 9 and -2

What is the final expression of the polynomial p(x) as a product of linear factors?

• (x + 6)(x + 3)(x - 6)

• (x + 6)(x + 6)(x - 3)

• (x + 6)(x - 3)(x - 3)

• (x + 6)(x - 6)(x + 3)

What is the purpose of rewriting a polynomial as a product of linear factors?

• To simplify the polynomial

• To change the polynomial's coefficients

• To find the roots of the polynomial

• To increase the degree of the polynomial