How do you factor #3f^2-2f-21#?

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Answer 1 · 2016-04-14T08:26:49

#color(blue)( (3f + 7 ) ( f - 3 ) # is the factorised form of the equation.

#3f^2 - 2f - 21#

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

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

#N_1*N_2 = a*c = 3*-21 = -63#

AND

#N_1 +N_2 = b = -2#

After trying out a few numbers we get #N_1 = -9# and #N_2 =7#
#7*(-9 )= -63#, and #7 + (-9)= -2#

#3f^2 - 2f - 21 = 3f^2 - 9f + 7f - 21#

# = 3f ( f - 3 ) + 7 ( f- 3 )#

# = (3f + 7 ) ( f - 3 ) #

#color(blue)( (3f + 7 ) ( f - 3 ) # is the factorised form of the equation.