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

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

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Answer 1 · 2018-08-09T13:17:24

$\Rightarrow (3 x + 5) (x - 4)$ $color(purple)(=> (3 x + 5) (x - 4)$

Explanation:

$3 {sin}^{2} y - 7 sin y - 20$ $3sin^2y - 7 sin y - 20$

Let $sin y = x$ $sin y = x$

$\Rightarrow 3 x^{2} - 7 x - 20$ $=> 3x^2 - 7x - 20$

$\Rightarrow 3 x^{2} - 12 x + 5 x - 20$ $=> 3x^2 - 12 x + 5 x - 20$

$\Rightarrow 3 x (x - 4) + 5 (x - 4)$ $=> 3 x (x - 4) + 5 (x - 4)$

$\Rightarrow (3 x + 5) (x - 4)$ $color(purple)(=> (3 x + 5) (x - 4)$

Answer 2 · 2018-08-09T14:13:50

$(sin y - 4) (3 sin y + 5)$ $(siny-4)(3siny+5)$

Explanation:

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

$the factors of the product 3 \times - 20 = - 60$ $"the factors of the product "3xx-20=-60$

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

$split the middle term using these factors$ $"split the middle term using these factors"$

$3 {sin}^{2} y - 12 sin y + 5 sin y - 20 \leftarrow factor by grouping$ $3sin^2y-12siny+5siny-20larrcolor(blue)"factor by grouping"$

$= 3 sin y (sin y - 4) + 5 (sin y - 4)$ $=color(red)(3siny)(siny-4)color(red)(+5)(siny-4)$

$take out the common factor (sin y - 4)$ $"take out the "color(blue)"common factor "(siny-4)$

$= (sin y - 4) (3 sin y + 5)$ $=(siny-4)(color(red)(3siny+5))$

$3 {sin}^{2} y - 7 sin y - 20 = (sin y - 4) (3 sin y + 5)$ $3sin^2y-7siny-20=(siny-4)(3siny+5)$

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

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