alleryStart learning →Factor: 9x^2 + 12x + 4.
A(3x+4)(3x+1)
B(9x+2)(x+2)
C(3x-2)(3x-2)
D(3x+2)(3x+2)
Answer & Solution
Correct answer: D. (3x+2)(3x+2)
1. Check that the first term 9x squared is a perfect square: it equals (3x) squared.
2. Check that the last term 4 is a perfect square: it equals 2 squared.
3. Check the middle term: twice the product of 3x and 2 is 12x, which matches.
4. Since all three checks pass, write the square of the binomial: (3x + 2)(3x + 2).
_Source: OpenStax Elementary Algebra (CC BY 4.0), Ch 7 "Factoring", section 7.4 Factor Special Products_
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