Question

factor: x² - 30x + 225
options:
(x - 15)²
(x - 25)²
(x + 15)²
(x + 25)²

Explanation:

Step1: Recall the perfect square formula

The perfect square trinomial formula is \((a - b)^2 = a^2 - 2ab + b^2\) and \((a + b)^2 = a^2 + 2ab + b^2\). For the quadratic \(x^2 - 30x + 225\), we compare with \(a^2 - 2ab + b^2\). Here, \(a = x\), so we need to find \(b\) such that \(2ab = 30x\) and \(b^2 = 225\).

Step2: Find the value of \(b\)

From \(b^2 = 225\), we get \(b=\sqrt{225}=15\) (since the middle term is \(- 30x=-2\times x\times15\), so \(b = 15\) and the sign is negative).

Step3: Apply the perfect square formula

Using \((a - b)^2\) with \(a = x\) and \(b = 15\), we get \((x - 15)^2\).

Answer:

\((x - 15)^2\) (corresponding to the green card option: \((x - 15)^2\))