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To recognize that a trinomial fits the Perfect Square Trinomials Pattern, which three checks must all pass?
AFirst term is a square, and the trinomial has no constant
BLast term is a square, and the leading coefficient is 1
CFirst term, last term are squares, and middle term equals 2ab
DMiddle term equals 2ab, and the constant term is even
Answer & Solution
Correct answer: C. First term, last term are squares, and middle term equals 2ab
1. The pattern requires three separate checks on the trinomial.
2. First, the leading term must be a perfect square, written as a squared.
3. Second, the last term must also be a perfect square, written as b squared.
4. Third, the middle term must equal exactly twice the product of a and b, or the trinomial does not fit the pattern.
_Source: OpenStax Elementary Algebra (CC BY 4.0), Ch 7 "Factoring", section 7.4 Factor Special Products_
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