How do you factor x^3 -7x + 6 = 0x3−7x+6=0?

1 Answer
Nghi N.
Apr 1, 2016

(x - 1)(x - 2)(x + 3)

Explanation:

f(x) = x^3 - 7x + 6f(x)=x3−7x+6
Since (a + b + c + d = 0), then f(1) = 0 --> one factor if (x - 1).
After division -->
f(x) = (x - 1)(x^2 + x - 6).f(x)=(x−1)(x2+x−6).
The trinomial in parentheses can be factored.
Find 2 numbers knowing sum (1) and product (-6). They are -2 and 3.
Therefor,
f(x) = (x - 1)(x - 2)(x + 3)f(x)=(x−1)(x−2)(x+3)

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