How do you factor #7x^2 + 51x + 14#?

1 Answer
Mar 14, 2016

Answer:

#(7x +2 ) (x +7) # is the factorised form of the expression.

Explanation:

#7x^2 + 51x +14#

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

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

#N_1*N_2 = a*c = 7*14 = 98 #

AND

#N_1 +N_2 = b = 51#

After trying out a few numbers we get #N_1 = 49# and #N_2 =2#

#49 * 2 = 98 #, and #49 + 2= 51#

#7x^2 + 51x +14 =7x^2 + 49x +2x +14#

#=7x (x +7) + 2 (x+7)#

#=(7x +2 ) (x +7) #

#(7x +2 ) (x +7) # is the factorised form of the expression.