How do you factor completely #−7x^2 + 14x − 21#?

1 Answer
Nghi N.
May 18, 2016

#-7(x^2 - 2x + 3)#

Explanation:

f(x) = -7y = -7(x^2 - 2x + 3)
D = d^2 = b^2 - 4ac = 4 - 12 = -8.
Since D < 0, the trinomial in parentheses can't be factored.
Therefor:
#f(x) = -7(x^2 - 2x + 3)#

NOTE. We can factor f(x) by using the 2 complex roots.
#d^2 = -8# --> #d = +- 2isqrt2#
#x = -b/(2a) +- d/(2a) = 2/2 +- (2isqrt2)/2 = 1 +- isqrt2#
The factored form will be:
#f(x) = -7(x - x1)(x - x2) = - 7(x - 1 + isqrt2)(x -1 - isqrt2)#

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