How do you use synthetic division to evaluate f(x) = x^3-3x^2+x-4 when x = 2?

Answer 1

Your problem is equivalent to

(x³ - 3x² + x - 4)/(x-2)

The coefficients of the numerator are 1, -3, 1, -4.

The solution is as follows:

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2 | 1 -3 1 -4 Set up the coefficients in decreasing power of x, and 2 is the divisor.

2 -2 -2

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1 -1 -1 -6

Here are the steps:

(a) Bring down the leading coefficient of 1.

(b) 2*1=2. Add -3 and 2 to obtain -1.

(c) 2*-1=-2. Add 1 and -2 to obtain -1.

(d) -1*2=-2. Add -2 and -4 to obtain -6

The quotient has the coefficients 1,-1,-1 so it is x² - x - 1. The remainder is -6.

Answer:

The result is x² - x - 1 - 6/(x-2).

You can verify that the answer is correct, because

(x-2)*(x² - x - 1) - 6 = x³ - 3x² + x - 4