How do you factor the trinomial #5t-50+t^2#?

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Answer 1 · 2015-12-12T14:48:56

#color(blue)( (t-5) (t+10)# is the factorised form of the expression.

#5t-50+t^2#

#t^2 +5t-50#

We can Split the Middle Term of this expression to factorise it.

In this technique, if we have to factorise an expression like #at^2 + bt + c#, we need to think of 2 numbers such that:

#N_1*N_2 = a*c = 1*-50 = -50#

AND

#N_1 +N_2 = b = 5#

After trying out a few numbers we get #N_1 = 10# and #N_2 =-5#

#10*(-5) = -50#, and #10+(-5)= 5#

#t^2 +color(blue)(5t)-50 = t^2 +color(blue)(10t-5t)-50#

# t(t+10) -5(t+10)#

#=color(blue)( (t-5) (t+10)#