# The synthetic algorithm

Note the cubic equation x3 - 6x2 + 11x - 6 = 0. I will claim that x = 1 constitutes a root of that equation ( replace x by 1 in the equation to verify ). Thus, the binomial (x - 1) will divide our cubic equation evenly, without remainder. Perform the division to obtain the quotient, which is a quadratic equation. Completely factor the resulting quadratic equation to obtain the remaining two roots of our cubic equation.

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#### Solution Preview

1^3-6*1^2+11*1-6 = 1-6+11-6 = 0, so x=1 is a root of x^3-6x^2+11x-6, and so (x-1) is a factor of it.

We can use long or synthetic division to divide x^3-6x^2+11x-6 by (x-1). The synthetic ...

#### Solution Summary

This posting offers help with factoring the resulting quadratic equation to obtain the remaining two roots of our cubic equation.

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