Question

1. $(4v^3 - 12v^2 + 6) div (v - 3)$

Explanation:

Step1: Use polynomial long division

Divide the leading term of the dividend \(4v^3\) by the leading term of the divisor \(v\), we get \(4v^2\). Multiply the divisor \(v - 3\) by \(4v^2\): \(4v^2(v - 3)=4v^3-12v^2\).
Subtract this from the dividend: \((4v^3 - 12v^2 + 6)-(4v^3 - 12v^2)=6\).

Step2: Write the result

The division gives a quotient of \(4v^2\) and a remainder of \(6\). So we can express the result as \(4v^2+\frac{6}{v - 3}\).

Answer:

\(4v^2+\frac{6}{v - 3}\)