Factoring Trinomials through Grouping Techniques

This video tutorial demonstrates how to factor a trinomial using the grouping method, which is more efficient than trial and error. It begins with factoring out the greatest common factor, then breaks down the expression for easier handling. The video explains how to identify numbers that multiply to a product and add to a middle term, and how to rewrite the expression for grouping. The tutorial concludes by emphasizing the efficiency of this method over others.

What is the primary advantage of the grouping method over trial and error?

• It can be used for any type of polynomial.

• It doesn't require any calculations.

• It guarantees the correct answer on the first try.

• It requires less time.

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

• Identify the middle term.

• Factor out the greatest common factor.

• Multiply the coefficient of the squared term by the constant.

• Write the expression in two sets of parentheses.

What is the greatest common factor factored out from the original trinomial?

• 5

• 2

• 17

• X

What do you multiply together to find two numbers that add up to the middle term?

• The constant and the middle term.

• The coefficients of the squared and linear terms.

• The greatest common factor and the middle term.

• The coefficient of the squared term and the constant.

Which numbers need to multiply to 30 and add up to 17 in the example?

• 3 and 10

• 5 and 6

• 2 and 15

• 1 and 30

What is the purpose of rewriting the middle term using two specific numbers?

• To simplify the trinomial.

• To prepare for factoring by grouping.

• To eliminate the greatest common factor.

• To find the roots of the trinomial.

What is factored out from the first two terms during the factoring by grouping step?

• A 17

• A 3X

• A 5

• A 2 and an X

What is factored out from the last two terms in the example?

• A 5

• An X

• A 17

• A 2

What common factor is placed next to the set of parentheses containing 2X and 5?

• 6X^2

• 3X - 1

• 3X + 1

• 2X + 5

Why is it recommended to multiply out the factored expression?

• To practice multiplication skills.

• To simplify the expression further.

• To find additional factors.

• To verify it matches the original trinomial.