Question

polynomial operations reteach (teacher manually grades)
what is the result of combining the terms represented by the tiles below?
$x^2$
$x$
$-x$
$-x$
$+1$
$+1$
$+1$
$+1$
$-1$
$x^2$
$-1$
$-1$
$x$
$x$
○ $x + 1$
○ $x^2 + 2x + 1$
○ $x^2 + x - 5$
○ $x + 5$

Explanation:

Step1: Group like $x^2$ terms

$\boldsymbol{x^2 + x^2 = 2x^2}$

Step2: Group like $x$ terms

$\boldsymbol{x + (-x) + (-x) + x + x = x}$

Step3: Group constant terms

$\boldsymbol{1+1+1+1 + (-1) + (-1) + (-1) = 1}$

Step4: Combine all simplified terms

$\boldsymbol{2x^2 + x + 1}$

Answer:

$\boldsymbol{2x^2 + x + 1}$ (matches the second option: $\boldsymbol{ x^2 + 2x + 1}$ is incorrect, the correct combined polynomial is $\boldsymbol{2x^2 + x + 1}$)