Polynomial Division B48Bb6

1. **State the problem:** We need to divide the polynomial $$32x^6 - 16x^4 + 12x^3 - 8x^2$$ by $$-4x^2$$. 2. **Recall the division rule for polynomials:** When dividing each term of a polynomial by a monomial, divide the coefficients and subtract the exponents of like bases. 3. **Divide each term separately:** $$\frac{32x^6}{-4x^2} = \frac{32}{-4} x^{6-2} = -8x^4$$ $$\frac{-16x^4}{-4x^2} = \frac{-16}{-4} x^{4-2} = 4x^2$$ $$\frac{12x^3}{-4x^2} = \frac{12}{-4} x^{3-2} = -3x$$ $$\frac{-8x^2}{-4x^2} = \frac{-8}{-4} x^{2-2} = 2$$ 4. **Combine the results:** $$-8x^4 + 4x^2 - 3x + 2$$ 5. **Final answer:** $$\boxed{-8x^4 + 4x^2 - 3x + 2}$$