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

2 Answers
Kalyanam S.
Aug 9, 2018

#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)#

Jim G.
Aug 9, 2018

#(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)#

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