Question

When doing synthetic division and a power is missing, what must be done so that the answer is correct? Explain.

A. Multiply the divisor by the missing power.
B. Divide the dividend by the missing power.
C. Fill the missing power with zero.
D. Subtract the missing power from the dividend.

Answer 1

In synthetic division, you should fill the missing power with zero to maintain the proper alignment of the polynomial's terms. Doing this allows for correct synthetic division without modifying the divisor or dividend in any other way.

Step-by-step explanation:

When doing synthetic division and a power is missing, the correct action is to fill the missing power with zero. Synthetic division relies on the coefficients of each term of the polynomial being in descending order of power. If a power is missing, a placeholder coefficient of zero must be inserted to maintain proper alignment of the terms during division. In this process, you do not multiply the divisor by the missing power, divide the dividend by the missing power, or subtract the missing power from the dividend.

Consider an example where we divide x3 - 2x + 4 by x - 1, and here x2 is missing. We write the dividend as x3 + 0x2 - 2x + 4 to correctly perform synthetic division. This ensures each power of x is accounted for sequentially.