Questions: 4x^2+12x+9

4x^2+12x+9
Transcript text: b.) $4 x^{2}+12 x+9$
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Solution

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Solution Steps

To solve the quadratic expression \(4x^2 + 12x + 9\), we can factor it if possible. This involves finding two binomials that multiply to give the original quadratic expression. We can use the method of completing the square or check if it is a perfect square trinomial.

Step 1: Identify the Quadratic Expression

We start with the quadratic expression given by

\[ 4x^2 + 12x + 9. \]

Step 2: Factor the Expression

To factor the expression, we look for two identical binomials. The expression can be rewritten as

\[ (2x + 3)^2. \]

This indicates that the quadratic is a perfect square trinomial.

Step 3: Write the Factored Form

Thus, the factored form of the quadratic expression is

\[ (2x + 3)(2x + 3). \]

Final Answer

The factored form of the expression \(4x^2 + 12x + 9\) is

\[ \boxed{(2x + 3)^2}. \]

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