Factoring Trinomials Using Grouping Technique

This video tutorial explains how to factor a trinomial using the grouping technique when the leading coefficient is not a common factor. It covers finding integers r and s whose product equals the product of the leading coefficient and the constant term, and whose sum equals the middle coefficient. The tutorial demonstrates rewriting the trinomial, grouping terms, factoring out common factors, and verifying the result.

What is the first step in factoring a trinomial using the grouping technique?

• Determine if 'a' is a common factor.

• Rewrite the trinomial as a product of binomials.

• Identify the coefficients of the trinomial.

• Find the greatest common factor of all terms.

What are the integers 'r' and 's' used for in the grouping technique?

• To find the greatest common factor.

• To simplify the trinomial.

• To rewrite the middle term of the trinomial.

• To determine the constant term.

For the trinomial 6y² - 13y + 5, what is the product of 'a' and 'c'?

• 30

• 13

• 11

• 5

Which pair of integers has a product of 30 and a sum of -13?

• (-1, -30)

• (-2, -15)

• (-3, -10)

• (-5, -6)

How is the middle term of the trinomial rewritten using 'r' and 's'?

• As a single term.

• As a product of two binomials.

• As a sum or difference of two terms.

• As a constant.

What is the greatest common factor of the first group in the trinomial 6y² - 3y?

• y

• 1

• 6y

• 3y

What is the common binomial factor in the expression after grouping?

• y - 1

• 2y - 1

• 3y - 5

• y + 5

What is the second binomial factor in the factored form of the trinomial?

• y + 1

• y - 5

• 3y - 5

• 2y + 1

What is the purpose of multiplying out the factored form?

• To determine the constant term.

• To find the greatest common factor.

• To verify the factored form is correct.

• To simplify the expression.

What is the result of combining like terms in the expanded form?

• 6y² - 13y + 5

• 6y² - 10y + 5

• 6y² - 3y + 5

• 6y² - 15y + 5