Factoring Trinomials: Key Concepts and Techniques

What should you always check first when beginning to factor a polynomial?

• Number of terms

• Whether it is a trinomial

• Greatest Common Factor (GCF)

• Leading coefficient

What method is used if the leading coefficient of a trinomial is not one?

• Synthetic division

• Grouping after modifying the middle term

• Quadratic formula

• Simple trinomial factoring

In the 'X' method, what does the top number represent when factoring ax^2 + bx + c?

• Sum of a and c

• Sum of b and c

• Product of a and b

• Product of a and c

What is the next step after rewriting the middle term using the 'X' method?

• Combine like terms

• Use the quadratic formula

• Identify the leading coefficient

• Factor by grouping

What does the 'X' method help to determine when factoring trinomials?

• The possible values of x

• The new terms to replace the middle term

• The discriminant

• The coefficients of the original polynomial

When factoring 3x^2 + 5x + 2, what is the first thing we check?

• The degree of the polynomial

• If it can be factored using the quadratic formula

• If there is a Greatest Common Factor (GCF)

• If it is a trinomial

In the context of the 'X' method, what does the bottom number represent?

• The coefficient of x^2

• The constant term

• The coefficient of x

• The product of the coefficients of x^2 and x

Which factoring method is applied when you have four terms in a polynomial?

• Factoring by grouping

• Simple trinomial factoring

• Factoring out the GCF

• Quadratic formula

What should be done if a polynomial does not have a common factor among all terms?

• Nothing, it cannot be factored

• Rewrite the polynomial

• Apply the quadratic formula

• Factor out a 1

What is the greatest common factor of 6, 9, and 27?

• 6

• 3

• 27

• 9