Factor Polynomial Bdcd8F

1. **State the problem:** Factor the polynomial $$2x^4 - 10x^2 + 8$$ completely. 2. **Identify the structure:** Notice that the polynomial is a quadratic in terms of $x^2$. Let $y = x^2$, then the polynomial becomes $$2y^2 - 10y + 8$$. 3. **Factor out the greatest common factor (GCF):** The GCF of the terms is 2, so factor it out: $$2(y^2 - 5y + 4)$$ 4. **Factor the quadratic inside the parentheses:** We need two numbers that multiply to 4 and add to -5. These numbers are -4 and -1. 5. **Write the factorization:** $$2(y - 4)(y - 1)$$ 6. **Substitute back $y = x^2$:** $$2(x^2 - 4)(x^2 - 1)$$ 7. **Factor the difference of squares:** $$x^2 - 4 = (x - 2)(x + 2)$$ $$x^2 - 1 = (x - 1)(x + 1)$$ 8. **Final factorization:** $$2(x - 2)(x + 2)(x - 1)(x + 1)$$ **Answer:** $$2(x - 2)(x + 2)(x - 1)(x + 1)$$