Final answer:
To divide the given polynomials, follow the long division method, dividing the highest degree term of the dividend by the highest degree term of the divisor. Continue the division until the degree of the resulting polynomial is less than the degree of the divisor. The quotient is 3x - 2 with a remainder of 0.
Step-by-step explanation:
Dividing Polynomials
To divide the given polynomials, you need to follow the long division method. Start by dividing the highest degree term of the dividend by the highest degree term of the divisor. In this case, (4x³)/(2x) = 2x². Multiply the divisor by this result, which gives you 2x(2x - 1) = 4x² - 2x. Subtract this product from the dividend. Repeat the process, dividing the resulting polynomial by the divisor until the degree of the resulting polynomial is less than the degree of the divisor.
Continuing with the division, (6x²-10x + 4) ÷ (2x - 1) = 3x - 2. This is the quotient of the division. The remainder is 0 since the degree of the resulting polynomial is less than the degree of the divisor.
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