Question

16—18. factor these “special case” polynomials.

1. $9x^{2}+12x+4$

$(3x^{2}+4x+4)$
$(3x + 2)^{2}$

Explanation:

Step1: Identify perfect square form

A perfect square trinomial follows $a^2+2ab+b^2=(a+b)^2$.
For $9x^2+12x+4$, note $9x^2=(3x)^2$, $4=2^2$.

Step2: Verify middle term

Check if $2ab=2(3x)(2)=12x$, which matches the given middle term.

Step3: Write factored form

Apply the perfect square trinomial rule.

Answer:

$(3x+2)^2$