Factor Theorem Checker

The factor theorem states that $(x - k)$ is a factor of $p(x)$ if and only if $p(k) = 0$. So to check whether $(x - 2)$ divides $p(x) = x^3 - 8$, just compute $p(2) = 0$, which confirms it is a factor.

Choose b, c, d to fix the cubic and slide candidate k. The lab evaluates $p(k)$; a green tick appears when $p(k) = 0$. Try $p(x) = x^3 - 4x^2 + x + 6$ and test k = -1, 2, 3 to find all factors.

Students plug in $k$ with the wrong sign. Remember: for the factor $(x - k)$, substitute $+k$, not $-k$. So $(x + 3)$ corresponds to $k = -3$, and you check $p(-3)$.

Factor theorem makes solving higher-degree equations much easier and is the basis for splitting middle terms. In real life it helps reverse-engineer recipes: if you know one ingredient ratio is a factor, the whole formula simplifies.