Factor Gcf 91997E

1. **State the problem:** Factor the greatest common factor (GCF) from the expression $$ht^2 - t^2 + 4ht^3$$. 2. **Identify the terms:** The terms are $$ht^2$$, $$-t^2$$, and $$4ht^3$$. 3. **Find the GCF of the coefficients:** The coefficients are $$1$$, $$-1$$, and $$4$$. The GCF of $$1$$, $$-1$$, and $$4$$ is $$1$$. 4. **Find the GCF of the variables:** - For $$h$$: present in $$ht^2$$ and $$4ht^3$$ but not in $$-t^2$$. - For $$t$$: present in all terms with powers $$t^2$$, $$t^2$$, and $$t^3$$. The smallest power is $$t^2$$. 5. **Therefore, the GCF is $$t^2$$**. 6. **Factor out $$t^2$$:** $$ht^2 - t^2 + 4ht^3 = t^2(\cancel{h} - \cancel{1} + 4h t^{\cancel{3-2}}) = t^2(h - 1 + 4ht)$$. 7. **Final factored form:** $$t^2(h - 1 + 4ht)$$.