Final answer:
To find the other factor, we can use the synthetic division method. By dividing the polynomial f(x) by (x+7), we find that the other factor is 9x² - 50x - 7.
Step-by-step explanation:
To find the other factor, we need to use synthetic division to divide the polynomial f(x) by (x+7). Synthetic division is a method of dividing polynomials that involves only the coefficients of the terms. We divide the polynomial by the factor (x+7) and use the resulting coefficients to form the other factor.
Step 1: Write down the coefficients of the polynomial in the synthetic division form.
Step 2: Bring down the first coefficient.
Step 3: Multiply the factor (x+7) by the value brought down, and write the result under the next coefficient.
Step 4: Add the values in the second column.
Step 5: Repeat steps 3 and 4 until all coefficients have been used.
Step 6: The resulting polynomial is the other factor, and in this case, it is 9x² - 50x - 7. Therefore, the other factor is 9x² - 50x - 7.