Question

question 12 (mandatory) (1 point)
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 \(x^2 + 2x + 1\)

For \(x^2 + 2x + 1\), we have \(a = x\) (since \(a^2=x^2\)) and \(2ab = 2x\). Substituting \(a = x\) into \(2ab = 2x\), we get \(2\times x\times b=2x\), so \(b = 1\) (because \(2xb = 2x\) implies \(b = 1\) when we divide both sides by \(2x\)). Also, \(b^2=1^2 = 1\), which matches the constant term.

Step3: Apply the Formula

Using the perfect square formula \((a + b)^2=a^2 + 2ab + b^2\) with \(a=x\) and \(b = 1\), we get \((x + 1)^2=x^2+2x + 1\).

Answer:

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