Final answer:
To divide the polynomial (6x^2 - 13x + 2) by (3x - 2), use polynomial long division. The quotient is 2x - 3.
Step-by-step explanation:
To divide the polynomial (6x2 - 13x + 2) by (3x - 2), we can use polynomial long division. The first step is to divide the highest degree term of the dividend, which is 6x2, by the highest degree term of the divisor, which is 3x. This gives us 2x as the first term of the quotient.
Next, we multiply the entire divisor, (3x - 2), by the 2x we found in the previous step, which gives us 6x2 - 4x. We subtract this product from the dividend, 6x2 - 13x + 2, to get a new polynomial, -9x + 2.
Now, we repeat the process with the new polynomial, -9x + 2, as the dividend and (3x - 2) as the divisor. We divide the highest degree term, -9x, by the highest degree term, 3x, to get -3 as the next term of the quotient.
We then multiply the entire divisor, (3x - 2), by the -3 we found in the previous step, which gives us -9x + 6. We subtract this product from -9x + 2 to get a new polynomial, -4.
Since the degree of the new polynomial, -4, is less than the degree of the divisor, 3x - 2, we stop the process and write the quotient as the final answer: 2x - 3.