Question

How do you factor the trinomial `2y^2 + 6y − 20`?

Answer 1

`(2y+10)(y-2)`

Explanation:

For `2y^2` we can only have:

`(2y+?)(y+?)`

It is just a matter of finding the other two for -20

Target Factors of 20`-> color(green)({1,20}, {2, 10} {4,5})`

Testing the factors:
`+-(color(blue)(2y)xxcolor(green)(?))+-(color(blue)(1y)xxcolor(green)(?))=6` for `6y`

`(y)color(white)(..........)(y)`
`+-color(brown)((color(blue)(2)xxcolor(green)(2))+-(color(blue)(1)xxcolor(green)(10))) -> +-(4)+-(10)-> -4+10=6 color(white)(..)color(red)("works")`

Check

`=> (2y+10)(y-2)`

`=2y^2-4y+10y-20`

`=2y^2+6y-20`