Final answer:
The given expression -8x^7 + 12x^5 - 20 divided by 4x^3 simplifies to -2x^4 + 3x^2 - 5/x^3 by dividing numerical coefficients and subtracting exponents for like variables.
Step-by-step explanation:
To divide the expression - 8x^7 + 12x^5 - 20 by 4x^3, we apply the Division of Exponentials rule. This rule tells us to divide the numerical coefficients and subtract the exponents for corresponding variables. Here is the step-by-step process:
- Divide -8 by 4 to get -2. Since both terms have the variable x, subtract the exponents: 7 - 3 = 4. This gives us the first term of the quotient: -2x^4.
- Next, divide 12 by 4, which is 3. Again, subtract the exponents for x: 5 - 3 = 2. This gives us the second term of the quotient: +3x^2.
- The last term does not have the variable x, so we simply divide -20 by 4x^3, but because we cannot divide a number by a variable that it does not contain, this term becomes a fraction, -5/x^3.
The simplified answer is: -2x^4 + 3x^2 - 5/x^3.