Questions: Factor the quadratic trinomial 4x^2+12x+9. Show your work.

Factor the quadratic trinomial 4x^2+12x+9. Show your work.
Transcript text: Factor the quadratic trinomial $4 x^{2}+12 x+9$. Show your work.
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Solution

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Solution Steps

To factor the quadratic trinomial \(4x^2 + 12x + 9\), we can use the method of completing the square or recognize it as a perfect square trinomial. In this case, we notice that the trinomial can be written as the square of a binomial.

Step 1: Identify the Quadratic Trinomial

We start with the quadratic trinomial given by \[ 4x^2 + 12x + 9. \]

Step 2: Factor the Trinomial

To factor the trinomial, we recognize that it can be expressed as a perfect square. We can rewrite it as \[ (2x + 3)^2. \]

Final Answer

The factored form of the quadratic trinomial \(4x^2 + 12x + 9\) is \[ \boxed{(2x + 3)^2}. \]

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