Factoring Polynomials Using the Box Method

The video tutorial explains the box method for factoring trinomials, using the example x^2 + 2x - 24. It begins with drawing a box divided into four parts, placing the first and last terms of the trinomial in specific boxes, and then finding factors of the constant term. The tutorial guides through placing these factors in the box to determine common factors across rows and columns. Finally, it verifies the solution by checking the multiplication of the derived binomials, ensuring the correct factorization of the original trinomial.

What is the first step in the box method of factoring?

• Identifying the middle term

• Multiplying the coefficients

• Finding the factors of the constant term

• Drawing a box and dividing it into four parts

What does the box method help to avoid in factoring trinomials?

• Subtraction

• Multiplication

• Guessing and checking

• Division

What do we multiply to find the product placed in the box?

• The coefficients of the first and last terms

• The middle term's coefficient

• The factors of the middle term

• The constant term and the coefficient of the middle term

What is the product of the coefficients in the example given?

• -2

• 24

• -24

• 2

Which factors of 24 sum up to the middle term in the example?

• 4 and 6

• 2 and 12

• 1 and 24

• 3 and 8

What is the significance of the placement of negative and positive signs in the box?

• To determine the sum of the middle term

• To ensure the product matches the original equation

• To identify the factors of the constant term

• To find the greatest common factor

What is the common factor of x^2 and -4x?

• -4

• x^2

• x

• 6

Which step involves finding the greatest common factor?

• Factoring by grouping

• Verifying the solution

• Placing the coefficients

• Drawing the box

What are the final factors of the expression x^2 + 2x - 24?

• x - 6 and x + 4

• x + 6 and x - 4

• x - 4 and x + 6

• x + 4 and x - 6

How do we verify the solution obtained from the box method?

• By multiplying the factors

• By dividing the original equation

• By subtracting the factors

• By adding the factors