Algebra 2 (Factoring Methods) Quiz

Study Notes

GCF Factoring

Involves finding the Greatest Common Factor (GCF) of a polynomial.
Divide each term by the GCF to determine the remaining factors within parentheses.

TRAM (Quadratic Trinomials)

Used when the leading coefficient is 1.
Begin with the square root of the first term for the new factors.
Identify two numbers that multiply to the constant term (c) and add up to the linear coefficient (b).

Tricky TRAM

Applicable when the leading coefficient is not equal to 1.
Calculate the product of the leading coefficient (a) and the constant (c).
Find factors of this product that sum to the linear coefficient (b).
Rewrite the trinomial using these factors, then group into pairs.
Apply the GCF method to factor each pair, resulting in two binomials.

Perfect Square Trinomial (PST)

A trinomial qualifies as a perfect square if:
- The first term is a perfect square.
- The last term is a positive perfect square.
- The middle term is double the product of the square roots of the first and last terms.

PST Factoring Method

If a trinomial is a perfect square, its factors can be expressed as (a+b)(a+b).

Difference of Two Squares (DOTS)

A binomial is a difference of two squares when both terms are perfect squares, and the operation is subtraction.

DOTS Factoring Method

The factors of a difference of two squares take the form (a+b)(a-b).

Sum of Perfect Cubes

A binomial qualifies as a sum of perfect cubes if both terms are perfect cubes and the operation is addition.
Its factors can be expressed as (a+b)(a^2-ab+b^2).

Difference of Perfect Cubes

A binomial is a difference of perfect cubes if both terms are perfect cubes and the operation is subtraction.
Its factors are represented as (a-b)(a^2+ab+b^2).

SOAP Method

SOAP stands for Same, Opposite, Always Positive.
This method is used for factoring sums and differences of perfect cubes.
For example, for a^3 + b^3, the factors are (a+b)(a^2-ab+b^2) with operation signs indicating same, opposite, and always positive.

Grouping Method

Group polynomials into pairs of terms.
Factor out the GCF from each pair.
If the remaining expressions in parentheses are identical, the polynomial can be factored as a combination of one common factor and the sum of the GCFs from each pair.

Description

Test your understanding of factoring methods in Algebra 2 with this quiz. From GCF factoring to the TRAM method for quadratic trinomials, this quiz covers essential techniques used in factoring polynomials. Perfect for students looking to reinforce their skills.