Question

which expression is equivalent to x^2 + 2x + 2?

Answer 1

To find an expression equivalent to \( x^2 + 2x + 2 \), we can complete the square or factor if possible.

1. **Completing the square**:

Take the quadratic \( x^2 + 2x + 2 \).

Start by focusing on the quadratic and linear terms:
\[
x^2 + 2x
\]
To complete the square, take half of the coefficient of \( x \) (which is 2), square it, and add and subtract that square inside the expression:
\[
x^2 + 2x + 1 - 1 + 2 = (x+1)^2 + 1
\]

Therefore, the expression \( x^2 + 2x + 2 \) can be rewritten as:
\[
(x+1)^2 + 1
\]

Thus, an equivalent expression to \( x^2 + 2x + 2 \) is:
\[
(x+1)^2 + 1
\]

Alternatively, if you want the expression in standard form, it is already given as \( x^2 + 2x + 2 \) and is not easily factorable in terms of integers.