How do you factor #2m ^ { 2} + 19m + 9#?

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Answer 1 · 2018-03-15T02:21:21

#m= -1/2 and m=-9#

#2m^2+19m+9#

multiply the first and last terms to for the number that you will find the factors of
#2m^2*9=18m^2#

find the numbers that multiply to 18 and add to 19
#1*18=18; 1+18=19#

put those numbers in place of the multiplied number you found and drop down the first and last term
#2m^2+18m+(1)m + 9#

group the terms into two groups of two using parentheses
#(2m^2+18m)+(m+9)#

factor the groups, the parentheses should both be the same
#2m(m+9)+1(m+9) #

the values in the parentheses are one of your answers, the ones outside are your other answer.
#m=(2m+1) ; m=(m+9)#

set them equal to zero to find the value
#0=2m+1 ;0=m+9#

#-1/2=m; -9=m#