How do you factor the trinomial #5r + r^2 - 14#?

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Answer 1 · 2016-03-25T18:04:46

#color(green)( (r -2) ( r + 7 ) # is the factorised form of the equation.

#r^2 + 5r -14#

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

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

#N_1*N_2 = a*c = 1* (- 14) = -14#

AND

#N_1 +N_2 = b = 5#

After trying out a few numbers we get #N_1 = 7# and #N_2 =-2#
#7*(-2) = -14#, and #7+(-2)= 5#

#r^2 + color(green)( 5r) -14 = r^2 + color(green)(7r -2r) -14#

#= r ( r+7 ) -2 ( r + 7)#

#= color(green)( (r -2) ( r + 7 ) #

#color(green)( (r -2) ( r+7 ) # is the factorised form of the equation.