Factoring Trinomials with the Box Method

The video tutorial explains how to factor a polynomial by multiplying the leading coefficient with the constant term and finding two numbers that multiply to this product and add to the middle coefficient. It introduces the box method to organize terms and calculate areas representing polynomial terms. The tutorial concludes with the final steps to factor the polynomial completely.

What is the product of the two numbers that need to be identified for factoring the polynomial?

• -7

• 30

• 7

• -30

What is the sum of the two numbers that these identified numbers need to add up to?

• -7

• 7

• 6

• -6

Which pair of numbers multiplies to -30 and adds to -7?

• -3 and -10

• 3 and 10

• -5 and -6

• 5 and 6

In the four-region box method, what terms are written to represent the split middle term?

• 10x and 3x

• -10x and -3x

• 10x and -3x

• -10x and 3x

What is the original polynomial reconstructed from the box method?

• 5x^2 - 7x + 6

• 5x^2 + 7x - 6

• 5x^2 - 7x - 6

• 5x^2 + 7x + 6

What does the area of each region in the box represent?

• Derivatives of the polynomial

• Possible solutions to the polynomial

• Factors of the polynomial

• Terms of the original polynomial

How is the term 5x^2 represented in the box?

• x multiplied by 5x

• 5x multiplied by x

• 1x multiplied by 5x

• 5 multiplied by x^2

What is the factored form of the polynomial?

• (5x + 3)(x - 2)

• (5x - 3)(x - 2)

• (5x + 3)(x + 2)

• (5x - 3)(x + 2)

Which term when multiplied by 3 gives a product of 3x?

• 1x

• x

• 3

• 10x

What must be true about the numbers used in the box method for factoring?

• They must add to the coefficient of the highest degree term.

• They must multiply to the constant term and add to the coefficient of the middle term.

• They must add to the constant term and multiply to the coefficient of the middle term.

• They must multiply to the coefficient of the highest degree term.