Question

How do you factor the trinomial `12k^2+15k=16k+20`?

Answer 1

The factors are: `(3k - 4)(4k+ 5)`

Explanation:

`12k^2-k-20=0`
Integer factors of 12 are: {1,12} , {2,6}, {3,4}

Integer factors of 20 are: {1,20}, {2,10}, {4,5}

The combination that could yield `12k^2` and `k` are
{3,4} for 12 and {4,5} for 20

Try-1
`(3k - 4)(4k+ 5) =12k^2 +15k -16k -20`

`color(green)("Struck lucky first try!")`

`12k^2+15k=16k+20 color(white)(xx) -> color(white)(xx)(3k - 4)(4k+ 5)=0`