Question

factor $0.04x^{2}+0.4x + 1$ using the perfect square trinomial method (if applicable).
a. $0.04(x^{2}+10)$
b. $(0.2x + 1)^{2}$
c. not a perfect square trinomial
d. $(0.2x - 1)^{2}$

Explanation:

Step1: Identify square terms

First term: $0.04x^2=(0.2x)^2$, last term: $1=1^2$

Step2: Verify middle term

Check $2\times0.2x\times1=0.4x$, matches given middle term.

Step3: Write perfect square

Form: $(a+b)^2=(0.2x+1)^2$

Answer:

b. $(0.2x + 1)^2$