Final answer:
To divide the polynomial (4v³-12v²+6) by (v-3), use polynomial long division to arrive at 4v² as the quotient, with 6/(v-3) as the remainder, thus the solution is 4v² + 6.
Step-by-step explanation:
To solve the division (4v³-12v²+6)÷(v-3), you can use polynomial long division or synthetic division. Given that there are no typos in the original polynomial, let's use polynomial long division.
First, divide the leading term of the numerator, 4v³, by the leading term of the denominator, v, to get 4v².
Multiply this result by the divisor (v-3) to get 4v³ - 12v², and subtract this from the original polynomial, which will give you the new polynomial 6.
Since there are no more terms in the numerator that contain variables, and since we have a constant (6) divided by a linear binomial (v-3), we can conclude that 6 is the remainder.
Therefore, the solution will be 4v² + 6.