Factoring Polynomials and Expressions

This video tutorial explains how to factor a quadratic polynomial by grouping. It begins with an introduction to the polynomial expression and its characteristics. The tutorial then demonstrates how to divide the polynomial into two groups and factor out the greatest common factor from each group. Finally, it shows how to factor the entire expression and verify the result by multiplying it back to its original form.

What is the degree of the polynomial expression discussed in the video?

• 2

• 1

• 4

• 3

Why is it important to have an even number of terms in the polynomial for factoring by grouping?

• To ensure symmetry

• To apply the technique correctly

• To make it a quadratic

• To simplify calculations

What is the simplified form of the given expression?

• x^2 - 11x + 18

• x^2 - 9x + 18

• x^2 - 10x + 18

• x^2 - 12x + 18

What is the first step in the factoring by grouping technique?

• Divide the polynomial into two halves

• Simplify the expression

• Combine like terms

• Factor out the greatest common factor

What is the greatest common factor of the first two terms in the expression?

• 18

• 9

• 2

• x

Why do we factor out a negative 9 instead of a positive 9 from the second half?

• To make calculations easier

• To ensure a common binomial factor

• To simplify the expression

• To change the sign of the terms

What is the common binomial factor in the expression?

• x - 2

• x + 2

• x + 9

• x - 9

What is the final factored form of the quadratic expression?

• (x - 2)(x - 9)

• (x + 2)(x - 9)

• (x - 2)(x + 9)

• (x + 2)(x + 9)

How can you verify that the expression is factored correctly?

• By simplifying the expression

• By comparing with another expression

• By checking the degree

• By multiplying the factors

What is the result of multiplying the factors (x - 2) and (x - 9)?

• x^2 - 12x + 18

• x^2 - 10x + 18

• x^2 - 9x + 18

• x^2 - 11x + 18