Question

1. factor $0.01x^{2} + 0.2x + 1$ using the perfect square trinomial method (if applicable).

a. $(0.1x + 1)^{2}$
b. $(0.01x - 1)^{2}$
c. $0.01(x^{2} + 20)$
d. not a perfect square trinomial

Explanation:

Step1: Identify trinomial components

Let $a^2=0.01x^2$, $b^2=1$, $2ab=0.2x$

Step2: Solve for $a$ and $b$

$a=\sqrt{0.01x^2}=0.1x$, $b=\sqrt{1}=1$

Step3: Verify $2ab$

$2ab=2\times0.1x\times1=0.2x$, matches the middle term

Step4: Write perfect square form

$(a+b)^2=(0.1x+1)^2$

Answer:

a. $(0.1x + 1)^2$