Question: $$x ^ { 2 } + 6 x + 9$$

Solution

To factor the quadratic expression \(x^2 + 6x + 9\), follow these steps: Identify the coefficients from the quadratic expression \(ax^2 + bx + c\). In this case, \(a = 1\), \(b = 6\), and \(c = 9\). Find two numbers that multiply to \(c\) (9) and add to \(b\) (6). These numbers are 3 and 3. Write the expression as a squared binomial: \[ (x + 3)(x + 3) \] Simplify the factored expression: \[ (x + 3)^2 \] So, the factored form of \(x^2 + 6x + 9\) is \((x + 3)^2\).