Question

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. not a perfect square trinomial
d. $0.01(x^{2}+20)$

Explanation:

Step1: Identify square terms

First term: $0.01x^2=(0.1x)^2$, last term: $1=1^2$

Step2: Verify middle term

Check if $2\times0.1x\times1=0.2x$, which matches the given middle term.

Step3: Apply perfect square formula

Use $a^2+2ab+b^2=(a+b)^2$, where $a=0.1x$, $b=1$.
Expression: $(0.1x + 1)^2$

Answer:

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