Questions and Answers
What method involves finding the greatest common factor (GCF) first?
What does TRAM stand for?
Quadratic Trinomials method where the leading coefficient is equal to 1
What is a Tricky TRAM?
Quadratic Trinomials method where the leading coefficient is not equal to 1
What conditions must be met for a trinomial to be a perfect square?
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What are the factors of a perfect square trinomial?
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What is DOTS?
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What are the factors of a difference of two squares?
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What are the factors of a sum of perfect cubes?
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What are the factors of a difference of perfect cubes?
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What does SOAP stand for?
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What is the first step in the grouping method of factoring?
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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.
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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.
