How do you solve # x^2 + 9x + 8 = 0# by factoring?

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Answer 1 · 2015-08-20T13:07:54

The solutions are
#color(blue)( x=-1#
#color(blue)(x=-8#

#x^2+9x+8=0#

We can Split the Middle Term of this expression to factorise it and thereby find solutions.

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 =1*8 =8#
and
#N_1 +N_2 = b = 9#

After trying out a few numbers we get #N_1 = 8# and #N_2=1#

#8*1 = 8#, and #8+ 1= 9#

#x^2+9x+8=x^2+8x+1x+8#

#x(x+8) +1(x+8)=0#

#color(blue)((x+1)(x+8))=0# is the factorised form of the equation.

Now we equate the factors to the R.H.S(0)
#x+1=0,color(blue)( x=-1#
#x+8=0, color(blue)(x=-8#