Question

question 12 (mandatory) (1 point) saved
what is the factored form of $x^2 + 2x + 1$

a) $(x - 1)^2$

b) $(x + 1)^2$

c) $(x + 2)^2$

d) $(x - 2)^2$

Explanation:

Step1: Recall perfect square formula

The perfect square trinomial formula is \( (a + b)^2 = a^2 + 2ab + b^2 \).

Step2: Identify \(a\) and \(b\) in \(x^2 + 2x + 1\)

Here, \(a = x\) (since \(a^2 = x^2\)) and \(2ab = 2x\). Substituting \(a = x\) into \(2ab = 2x\), we get \(2(x)b = 2x\), so \(b = 1\) (and \(b^2 = 1^2 = 1\), which matches the constant term).

Step3: Apply the formula

Using the perfect square formula with \(a = x\) and \(b = 1\), we have \(x^2 + 2x + 1=(x + 1)^2\). We can also check the other options:

• For option a: \((x - 1)^2=x^2-2x + 1\), which does not match.
• For option c: \((x + 2)^2=x^2+4x + 4\), which does not match.
• For option d: \((x - 2)^2=x^2-4x + 4\), which does not match.

Answer:

b) \((x + 1)^2\)