How do you factor?

Question

m^2-11m+18=0

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Answer 1 · 2018-05-24T05:04:16

Factors are: #(m-2)(m-9)=0#
#m=2#
#m=9#

Trying to factor by splitting the middle term:

Step 1
Factoring #m^2-11m+18#

The first term is, #m^2# its coefficient is #1# .
The middle term is, #-11m# its coefficient is #-11# .
The last term, "the constant", is #+18#

Step 2
Find two factors of #18# whose sum equals the coefficient of the middle term, which is #-11# .

#-18 + (-1) = -19 #
#-9 + (-2) = -11 -----> This is the one

Step 3
Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -9 and -2
#m^2 - 9m - 2m +18#

#m(m-9) - 2(m-9)# ------> pulling out the like factors

#(m-2).(m-9) = 0#

#m-2=0# -------> #color(red)(m=2)#

#m-9=0# ------->. #color(red)(m=9)#