How do you use the factor theorem to determine whether x+4 is a factor of #2x^3 + x^2 - 25x + 12 #?

1 Answer
Alan P.
Jan 23, 2016

Since when #x=-4# then #2x^3+x^2-25x+12=0#
by the factor theorem #(x+4)# is a factor.

Explanation:

The factor theorem says that for an expression #f(x)#
then #(x-a)# is a factor of #f(x)# if and only if #f(a)=0#

Note that #(x+4) = (x- color(red)((-4)))#

So we evaluate
#color(white)("XXX")f(color(red)(-4)) = 2(-4)^3+-4)^2-25(-4)+12#

#color(white)("XXXXXXX")=-128 +16 +100 +12#

#color(white)("XXXXXXX")=0#

and discover that #(x-(-4)) = (x+4)# is a factor of the given expression.

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