How do you factor the trinomial #2x^2 +11x + 9#?

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Answer 1 · 2016-05-16T16:58:35

# color(blue)( (2x + 9) (x + 1) # is the factorised form of the expression.

#2x^2 + 11x + 9 #

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 = 2 * 9 = 18#

AND

#N_1 +N_2 = b = 11#

After trying out a few numbers we get #N_1 = 9# and #N_2 =2#

#9 * 2 = 18 #, and # 2 + 9 = 11#

#2x^2 + 11x + 9 = 2x^2 + 2x + 9x + 9 #

# = 2x(x + 1) + 9( x + 1 )#

#(x+1)# is a common factor to each of the terms
# = color(blue)( (2x + 9) (x + 1) #