Question

question
find the quotient of $20t^4 - 12t^3 + 8t^2$ divided by $4t^2$.

Explanation:

Step1: Divide each term by \(4t^2\)

For the first term \(20t^4\div4t^2\), we use the rule of exponents \(a^m\div a^n = a^{m - n}\) and the coefficient division \(20\div4 = 5\), so \(20t^4\div4t^2=5t^{4 - 2}=5t^2\).

For the second term \(- 12t^3\div4t^2\), the coefficient division is \(-12\div4=-3\) and the exponent operation is \(t^{3-2}=t\), so \(-12t^3\div4t^2 = - 3t\).

For the third term \(8t^2\div4t^2\), the coefficient division is \(8\div4 = 2\) and the exponent operation is \(t^{2-2}=t^0 = 1\), so \(8t^2\div4t^2=2\).

Step2: Combine the results

Combining the three results from step 1, we get \(5t^2-3t + 2\).

Answer:

\(5t^2-3t + 2\)