Synthetic division is quick and not difficult to learn. The number in the upper left box is the value of x you're evaluating the function for (1). The remaining numbers across the top are the coefficients of the polynomial in decreasing order by power (the way they are written in standard form). The number at lower left is the same as the number immediately above it—the leading coefficient of the polynomial.

Each number in the middle row is the product of the x-value (the number at upper left) and the number in the bottom row just to its left. The number in the bottom row is the sum of the two numbers above it.

So, the number below -4 is the product of x (1) and 1 (the leading coefficient). That 1 is added to -4 to give -3 on the bottom row. Then that is multiplied by 1 (x, at upper left) and written in the next column of the middle row. This proceeds until you run out of numbers.

The last number, at lower right, is the "remainder", also the value of f(x). Here, it is 2 (not 0) for x=1, so f(1) = 2.

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3 years ago