Question

which expression does not factor?
$m^3 + 1$
$m^3 - 1$
$m^2 + 1$
$m^2 - 1$
done

Explanation:

Step1: Factor sum of cubes

$m^3 + 1 = (m+1)(m^2 - m + 1)$

Step2: Factor difference of cubes

$m^3 - 1 = (m-1)(m^2 + m + 1)$

Step3: Check quadratic sum

$m^2 + 1$ has no real factors (it is a sum of squares, which does not factor over real numbers)

Step4: Factor difference of squares

$m^2 - 1 = (m+1)(m-1)$

Answer:

$\boldsymbol{m^2 + 1}$