Question

When the function f(x) is divided by 3a + 1, the quotient is 2x² - 9x 1 and the remainder is -2. Find the function f(x) and write the result in standard form.

Answer 1

To find the function f(x), use long division with the divisor 3a + 1. The quotient is 2x² - 9x - 1 and the remainder is -2.

Step-by-step explanation:

To find the function f(x), we need to perform long division. The divisor is 3a + 1, the quotient is 2x² - 9x - 1, and the remainder is -2. To divide, we divide the first term of the dividend (2x²) by the first term of the divisor (3a). This gives us 2/3a * x² = 2/3ax². We then multiply this by the divisor, giving us 2/3ax³. We subtract this from the original dividend and continue with the next terms until we get the remainder of -2. Therefore, the function f(x) is 2x² - 9x - 1 with a remainder of -2.