Factoring Quadratic Expressions

This video tutorial explains how to factor a quadratic polynomial by grouping. It begins with an introduction to the polynomial expression and the necessity of having an even number of terms. The tutorial then outlines the steps for factoring by grouping: dividing the polynomial into two halves, factoring out the greatest common factor from each group, and factoring out the common binomial factor. The video concludes with a verification of the factored form and a summary of the process.

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

• 3

• 4

• 2

• 1

Why is it important to have an even number of terms in the polynomial?

• To simplify the expression

• To use the technique of factoring by grouping

• To find the roots easily

• To apply the quadratic formula

What is the simplified form of the given expression?

• x^2 - 9x + 18

• x^2 - 2x + 18

• x^2 - 11x + 18

• x^2 - 11x - 18

What is the first step in factoring by grouping?

• Factor out the greatest common factor

• Divide the polynomial into two halves

• Multiply the terms

• Combine like terms

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

• x

• 2

• 9

• 18

Why do we factor out a negative 9 instead of a positive 9?

• To simplify the expression

• To ensure a common binomial factor

• To make the expression positive

• To reduce the degree of the polynomial

What is the common binomial factor in the expression?

• x - 2

• x - 9

• x + 9

• x + 2

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 the factored form is correct?

• By subtracting the terms

• By dividing the expression

• By multiplying the factors

• By adding the terms

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

• x^2 - 7x + 18

• x^2 - 11x + 18

• x^2 - 7x - 18

• x^2 - 11x - 18