Question

1. factor $0.09x^{2} + 0.6x + 1$ using the perfect square trinomial method (if applicable).

a. $(0.3x + 1)^{2}$
b. not a perfect square trinomial
c. $(0.3x - 1)^{2}$
d. $0.09(x^{2} + \frac{20}{3}x + \frac{100}{9})$

Explanation:

Step1: Identify $a^2$ term

$a^2 = 0.09x^2 \implies a = 0.3x$

Step2: Identify $b^2$ term

$b^2 = 1 \implies b = 1$

Step3: Verify middle term

$2ab = 2 \times 0.3x \times 1 = 0.6x$, matches given middle term.

Step4: Write perfect square form

$(a + b)^2 = (0.3x + 1)^2$

Answer:

a. $(0.3x + 1)^2$