Factoring Trinomials Using the Reverse FOIL Method Practice

Practice Objectives

Demonstrate the ability to factor out the GCF from a polynomial
Demonstrate the ability to factor a trinomial when a ≠ 1

Practice Factoring Trinomials When the Leading Coefficient is not 1

Instructions:

Answer 7/10 questions correctly to pass.

Factor each trinomial using the AC Method, then complete the "Factored Form" by entering the values for "a", "b", "c", and "d" below. If the polynomial is prime, select the "Prime Polynomial" checkbox.

The first term of each binomial must be positive
Negative values for "a" or "c" will trigger an "invalid number" error

Problem:

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Factoring Trinomials Using the AC Method (Grouping):

Factor out the GCF if it isn't 1
- If the leading coefficient is negative, factoring out the -GCF is helpful
Write the trinomial in standard form
- ax² + bx + c
Find two integers whose product is ac and whose sum is b
Use the two integers to rewrite the middle-term
Factor the four-term polynomial using grouping
If no such integers can be found, the polynomial is prime

Factoring Trinomials Using the Reverse FOIL Method:

Factor out the GCF if it isn't 1
- If the leading coefficient is negative, factoring out the -GCF is helpful
Write the trinomial in standard form:
- ax² + bx + c
Think about the possible factor pairs of "a", the leading coefficient
- We generally use positive factor pairs to make our work easier
- Let's call the integers p and q for reference
- Set up the two binomials using p and q:
  - (px + __)(qx + __)
Think about the possible factor pairs of "c", the constant term
- Let's call these integers m and n for reference
- Fill in the blanks, then check if the sum of the outer and inner products equals the middle term (bx)
- If it does, then: ax² + bx + c = (px + m)(qx + n)
If all factor combinations have been tested and none work, the polynomial is prime