Polynomial Division and Factoring Concepts

The video tutorial explains how to factor a polynomial with a known factor of x+2. It begins by dividing the polynomial by the known factor to simplify the expression. The tutorial then focuses on factoring the resulting quadratic expression using methods like grouping. Finally, the polynomial is expressed as a product of linear factors, completing the factorization process.

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

• x + 1

• x + 2

• x - 2

• x - 1

What is the first step in dividing the polynomial by x + 2?

• Divide the highest degree term by x

• Subtract x + 2 from the polynomial

• Multiply the polynomial by x + 2

• Add x + 2 to the polynomial

What is the result of subtracting 22x from 19x during the division process?

• -3x

• -41x

• 3x

• 41x

What is the purpose of bringing down terms during polynomial division?

• To simplify the expression

• To add more terms

• To eliminate the remainder

• To continue the division process

What is the significance of having no remainder in polynomial division?

• The polynomial is prime

• The division was incorrect

• The divisor is not a factor

• The divisor is a factor

After dividing by x + 2, what type of expression is left?

• Constant expression

• Quadratic expression

• Linear expression

• Cubic expression

What method is suggested for factoring the quadratic expression?

• Quadratic formula

• Factoring by grouping

• Completing the square

• Synthetic division

What are the two numbers needed for factoring by grouping?

• Positive 10 and negative 2

• Positive 11 and negative 1

• Positive 9 and negative 3

• Positive 12 and negative 1

Why is factoring by grouping used in this scenario?

• The polynomial is already factored

• The leading coefficient is not 1

• The polynomial is linear

• The leading coefficient is 1

What is the final product of linear factors for p(x)?

• (x + 2)(x - 3)(4x + 1)

• (x + 2)(x + 3)(4x - 1)

• (x + 2)(x + 3)(4x + 1)

• (x + 2)(x + 1)(4x - 1)