Diamond Method in Factoring

The video tutorial explains the diamond method for factoring quadratic equations, particularly when the coefficient of 'a' is not one. The method involves creating a template with a product of 'a' and 'c' at the top, 'b' at the bottom, and finding factors that sum to 'b'. An example is provided using the equation 12x^2 - 4x - 5, demonstrating how to find factors, simplify ratios, and verify the solution by multiplying the binomials back together.

What is the primary purpose of the diamond method in factoring?

• To factor quadratic equations with a leading coefficient other than one

• To simplify fractions

• To factor quadratic equations with a leading coefficient of one

• To solve linear equations

In the diamond method, what is placed in the top space of the template?

• The value of b

• The value of a

• The product of a and c

• The sum of a and c

What is the role of the bottom space in the diamond method template?

• To hold the value of c

• To hold the sum of a and b

• To hold the value of b

• To hold the product of a and c

When using the diamond method, what do the sides of the template represent?

• The value of c

• Ratios involving ax

• The product of a and b

• The sum of a and b

In the example 12x squared minus 4x minus 5, what is the product of a and c?

• 48

• -60

• -48

• 60

What is the value of b in the equation 12x squared minus 4x minus 5?

• 12

• 5

• -4

• -5

Which pair of factors of -60 sum to -4 in the example?

• 6 and 10

• -6 and 10

• 6 and -10

• -6 and -10

What is the simplified form of the ratio 12x/6?

• 1x/2

• 12x/1

• 6x/1

• 2x/1

What is the simplified form of the ratio 12x/-10?

• 6x/-5

• 6x/5

• 12x/-5

• 12x/5

What are the binomials obtained after simplifying the ratios in the example?

• 2x + 1 and 6x + 5

• 2x + 1 and 6x - 5

• 2x - 1 and 6x + 5

• 2x - 1 and 6x - 5