Final answer:
The synthetic division form of the long division problem x² - 3x + 4 divided by x - 5 is represented by using the divisor's constant term with the opposite sign (+5) followed by the coefficients of the polynomial (1, -3, 4).
Step-by-step explanation:
The student has asked which option represents the synthetic division form of the long division problem x² - 3x + 4 divided by x - 5. When performing synthetic division, we use the opposite sign of the divisor's constant term. Therefore, since we are dividing by x - 5, we use +5 in the synthetic division process. The coefficients of the polynomial being divided (¹x², -3x, +4) should be used in their exact order. This information suggests that the correct synthetic division setup would involve starting with +5 and using the coefficients 1, -3, and +4. As such, the answer would be: 5 divided by 1 -3 4.