Factoring Polynomials and Long Division

The video tutorial explains how to factor a polynomial using long division. It begins with identifying a factor through trial and error, then sets up the polynomial for long division. The instructor demonstrates the long division process step-by-step, ensuring each term is eliminated correctly. Finally, the factorization is completed, resulting in the polynomial being expressed as a product of binomials.

What is the first step in factoring a polynomial using long division?

• Multiply the polynomial by a constant

• Find the derivative of the polynomial

• Identify a factor of the polynomial

• Divide the polynomial by a constant

Which method is used to find a factor of the polynomial?

• Integration

• Graphical method

• Synthetic division

• Trial and error

What is the factor of the polynomial if x = 1 is a root?

• x - 1

• x + 2

• x - 2

• x + 1

How is the polynomial set up for long division?

• As a quadratic

• As a trinomial

• As a binomial

• As a monomial

What is the first term you need to eliminate in long division?

• The cubic term

• The quadratic term

• The constant term

• The linear term

What do you multiply x by to get x cubed in the first step of long division?

• 2x

• x

• x squared

• 3x

What is the result of subtracting x cubed from x cubed?

• x cubed

• Zero

• x squared

• x

What is the next term to bring down after eliminating x cubed?

• 2x squared

• 3x squared

• x

• x squared

What do you multiply x by to get 3x squared?

• x squared

• 3x

• 2x

• x

What is the result of subtracting 3x from 3x?

• x

• 3x

• Zero

• 2x