Factor the polynomial $h^4 + 4h^2 - 12$ by using substitution.

Step 1: Notice that the variable part of the first term, $h^4$, is the square of the variable part of the middle term, $h^2$. Let $u = h^2$. Step 2: Substitute $u$ into the expression to rewrite it as a quadratic trinomial: $u^2 + 4u - 12$ Step 3: Factor the trinomial in terms of $u$. Find two numbers that multiply to $-12$ and add to $4$. These numbers are $6$ and $-2$: $(u + 6)(u - 2)$ Step 4: Replace $u$ with the original substitution, $h^2$: $(h^2 + 6)(h^2 - 2)$ Step 5: Check by multiplying: $(h^2 + 6)(h^2 - 2) = h^4 - 2h^2 + 6h^2 - 12 = h^4 + 4h^2 - 12$ ✓

The factored form is $(h^2 + 6)(h^2 - 2)$.