(x-1)(x-2)(x-3).
Use FOIL on the last two parenthetical expressions,
leave the first alone:
(x-1)(x²-3x-2x+6)
Combine -3x and -2x as -5x
(x-1)(x²-5x+6)
Multiply every term in (x-1) by every term in (x²-5x+6)
x³-5x²+6x-x²+5x-6
Combine -5x² and -x² as -6x²
Combine +6x and +5x as +11x
x³-6x²+11x-6
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The sum of the roots of a polynomial is
The coefficient of the term whose exponent of x is exactly
1 less than the largest exponent of x in the entire polynomial,
with the opposite sign.
x³+2x²-11x-12
The largest exponent of x is 3, found in the term x³. So the
term whose exponent of x is 1 less than 3, is the term +2x².
Its coefficient is +2, so we change its sign, and the sum of
the roots of the polynomial is -2.
Edwin
