How do you factor completely #t^3+t^2-22t-40#?

1 Answer
Alan P. · Shwetank Mauria
Mar 2, 2017

#t^3+t^2-22t-40=color(green)((t+2)(t+4)(t-5))#

Explanation:

Using the Rational Root Theorem, the possible roots of the given polynomial are contained in the set:
#color(white)("XXX"){+-1,+-2,+-4,+-8,+-10,+-20}#

Evaluating the given polynomial for each possible root (I chose to use a spread sheet to do this; see below)
we can determine the roots: #-2, -4, and +5#
#color(white)("XXX")#note that since the polynomial is of degree 3
#color(white)("XXXXX")#there can be a maximum of 3 unique roots.

which implies the factors:
#color(white)("XXX")(t+2)(t+4)(t-5)#

enter image source here

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