Question

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

Answer 1

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

Explanation:

`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`