Question

factor (0.25x^{2}+1.0x + 1.0) using the perfect square trinomial method (if applicable).
a. ((0.5x - 1)^{2})
b. (0.25(x^{2}+4))
c. not a perfect square trinomial
d. ((0.5x + 1)^{2})

factor (0.04x^{2}+0.28x + 0.49) using the perfect square trinomial method (if applicable).
a. not a perfect square trinomial
b. (0.04(x^{2}+7x + 12.25))
c. ((0.2x - 0.7)^{2})
d. ((0.2x + 0.7)^{2})

Explanation:

Problem 1:

Step1: Identify $a,b$ for trinomial

For $ax^2+bx+c$, $a=0.25, b=1.0, c=1.0$

Step2: Check perfect square condition

Verify $(\sqrt{a}x)^2 + 2\sqrt{a}\sqrt{c}x + (\sqrt{c})^2$:
$\sqrt{0.25}=0.5$, $\sqrt{1.0}=1$, $2*0.5*1=1.0=b$

Step3: Write factored form

$(0.5x + 1)^2$

Problem 2:

Step1: Identify $a,b$ for trinomial

For $ax^2+bx+c$, $a=0.04, b=0.28, c=0.49$

Step2: Check perfect square condition

Verify $(\sqrt{a}x)^2 + 2\sqrt{a}\sqrt{c}x + (\sqrt{c})^2$:
$\sqrt{0.04}=0.2$, $\sqrt{0.49}=0.7$, $2*0.2*0.7=0.28=b$

Step3: Write factored form

$(0.2x + 0.7)^2$

Answer:

1. d. $(0.5x + 1)^2$
2. d. $(0.2x + 0.7)^2$