How do you factor #y= 2x^2 + 13x + 15 # ?

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Answer 1 · 2015-12-10T05:27:40

# color(blue)((2x+3) (x+5) # is the factorised form of the expression.

#y=2x^2+13x+15#

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*15 =30#

AND

#N_1 +N_2 = b = 13#

After trying out a few numbers we get #N_1 = 10# and #N_2 =3#
#10*3 =30#, and #10+3 = 13#

#2x^2+color(blue)(13x)+15 =2x^2+color(blue)(10x +3x)+15 #

#=2x(x+5) +3(x+5) #

#= color(blue)((2x+3) (x+5) #