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Does 9x^2 + 50x + 25 fit the Perfect Square Trinomials Pattern?
AYes, since the first and last terms are both squares
BNo, since 25 is not a perfect square
CNo, since twice the cross product is 30x, not 50x
DYes, since twice the cross product is exactly 50x
Answer & Solution
Correct answer: C. No, since twice the cross product is 30x, not 50x
1. Check that the first and last terms are perfect squares: 9x squared is (3x) squared, and 25 is 5 squared, so both pass.
2. Check the middle term: twice the product of 3x and 5 is 30x.
3. The actual middle term is 50x, and 30x does not equal 50x, so the trinomial does not fit the perfect square pattern.
4. Since the pattern fails, factor using the ac method instead: 9 times 25 is 225, and 5 and 45 multiply to 225 and add to 50, giving (9x + 5)(x + 5) after splitting and grouping.
_Source: OpenStax Elementary Algebra (CC BY 4.0), Ch 7 "Factoring", section 7.4 Factor Special Products_
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