Question

How do you factor and simplify `3sin^2y-7siny-20`?

Answer 1

`color(purple)(=> (3 x + 5) (x - 4)`

Explanation:

`3sin^2y - 7 sin y - 20`

Let `sin y = x`

`=> 3x^2 - 7x - 20`

`=> 3x^2 - 12 x + 5 x - 20`

`=> 3 x (x - 4) + 5 (x - 4)`

`color(purple)(=> (3 x + 5) (x - 4)`

Answer 2

`(siny-4)(3siny+5)`

Explanation:

`"this is a quadratic in sine and is factored in the same"`
`"way as a normal quadratic"`

`"the factors of the product "3xx-20=-60`

`"which sum to "-7" are "-12" and "+5`

`"split the middle term using these factors"`

`3sin^2y-12siny+5siny-20larrcolor(blue)"factor by grouping"`

`=color(red)(3siny)(siny-4)color(red)(+5)(siny-4)`

`"take out the "color(blue)"common factor "(siny-4)`

`=(siny-4)(color(red)(3siny+5))`

`3sin^2y-7siny-20=(siny-4)(3siny+5)`