Factoring Trinomials Using the Rainbow Method

The video tutorial introduces the rainbow method for factoring trinomials with a lead coefficient greater than one. It explains the criteria for using this method and provides a detailed, step-by-step guide on how to apply it. The tutorial also covers factoring by grouping and demonstrates the process with an example problem, emphasizing the importance of matching binomials.

What is the lead coefficient in a trinomial?

• The sum of all coefficients

• The coefficient of the last term

• The coefficient of the first term

• The coefficient of the middle term

When is it appropriate to use the Rainbow Method?

• When the lead coefficient is 1

• When there is a greatest common factor

• When the trinomial is already factored

• When the lead coefficient is greater than 1 and no greatest common factor

What is the first step in the Rainbow Method?

• Subtract the last term from the first term

• Multiply the first and last coefficients

• Add the coefficients

• Divide the middle term by the lead coefficient

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

• 3 and 10

• 5 and 6

• 2 and 15

• -3 and 10

What is the purpose of splitting the middle term?

• To simplify the trinomial

• To eliminate the lead coefficient

• To create two binomials

• To prepare for factoring by grouping

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

• 5x

• 6x

• 2x

• 3x

What should be done after factoring by grouping?

• Add the binomials

• Multiply the binomials

• Factor out the common binomial

• Divide the binomials

In the second example, what is the product of the first and last terms?

• 60

• 75

• 45

• 90

Which numbers multiply to 60 and add to 17 in the second example?

• 6 and 10

• 5 and 12

• 3 and 20

• 4 and 15

What is the final factored form of the trinomial in the second example?

• (3x+5)(2x-1)

• (5x-1)(3x+4)

• (4x+3)(5x-1)

• (2x+3)(3x+5)