How do you factor #t^{2}+3t-10=0#?

1 Answer
Douglas K.
Oct 20, 2016

#(t + 5)(t -2)#

Explanation:

The factors are of the form:

#(t square a)(t squareb)#

Because the sign of the constant term #(-10)# is negative, you know that one of the #square#s will be positive and the other will be negative:

#(t + a)(t -b)#

You know that #(+ a)(- b) = 10# and a - b = 3, there are only two whole number that will do this: a = 5 and -b = -2

#(t + 5)(t -2)#

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