Asterisk Method for Factoring Trinomials

This video tutorial explains the asterisk method for factoring quadratic trinomials, especially when the leading coefficient is not one. It begins with factoring out the greatest common factor (GCF) and then uses the asterisk method to find two numbers that multiply to a specific product and add to a specific sum. The tutorial provides a step-by-step guide, including drawing an X and using a factor chart, to simplify the process and avoid common mistakes. The final factorization is verified to ensure accuracy.

What is the first step in using the asterisk method for factoring a quadratic trinomial?

• Multiply a and c

• Identify the leading coefficient

• Check for a greatest common factor

• Draw an X and axis

Why is it important to factor out the greatest common factor first?

• It simplifies the trinomial

• It changes the leading coefficient to one

• It makes the trinomial a perfect square

• It eliminates the need for the asterisk method

What should you do after factoring out the greatest common factor?

• Solve the trinomial using the quadratic formula

• Ignore the factor and focus on the remaining trinomial

• Multiply the factor back into the trinomial

• Use the guess and check method

What is the purpose of drawing an X and axis in the asterisk method?

• To organize the factors of the trinomial

• To visually represent the quadratic formula

• To separate the terms of the trinomial

• To help guess the factors

In the asterisk method, what do you place at the top of the X?

• The greatest common factor

• The value of b

• The product of a and c

• The sum of a and c

What do you place at the bottom of the X in the asterisk method?

• The product of a and c

• The value of b

• The greatest common factor

• The sum of a and c

How do you find the two numbers needed in the asterisk method?

• By guessing and checking

• By solving a system of equations

• By dividing the leading coefficient

• By using a factor chart

What is the relationship between the two numbers you find in the asterisk method?

• They multiply to b and add to a

• They multiply to the product of a and c and add to b

• They multiply to a and add to c

• They multiply to c and add to a

What should you do if the fractions formed by the numbers can be simplified?

• Leave them as they are

• Multiply them by the greatest common factor

• Simplify them before writing the factors

• Add them to the original trinomial

What is the final step in the asterisk method?

• Divide the factors by the leading coefficient

• Add the factors to the original equation

• Write the factors as a single trinomial

• Check the factors by multiplying them