Factor this: sin^2x - 0.3sinx - 0.04
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Factor this: sin^2x - 0.3sinx - 0.04

[From: ] [author: ] [Date: 12-08-05] [Hit: ]
3sinx - 0.= (2 sin x + 0.2)(0.5 sin x - 0.sin²x -0.3sinx - 0.......
Helppp i am stuck.

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sin^2x - 0.3sinx - 0.04

= 1/100 [ 100 sin^2(x) - 30 sin(x) - 4 ]

= 1/100 [ 100sin^2(x) - 40 sin(x) + 10sin(x) - 4 ]

= 1/100 [ 20 sin x (5 sin x - 2) + 2( 5 sin x - 2) ]

= 1/100 (20 sin x + 2)(5 sin x - 2)

= (2 sin x + 0.2)(0.5 sin x - 0.2)

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               sin²x - 0.3sinx - 0.04            ← First, factor out 0.01 or 1/100

           0.01(100sin²x - 30sinx - 4)            ← We can, also, factor out 2 now

           0.02(50sin²x - 15sinx - 2)     ← Now, we need two factors of 50(-2), i.e. -100,
                                                          that add to -15. Those would be -20 & +5

     0.02[50sin²x + 5sinx - 20sinx - 2]            ← Rewrote the middle term -15sinx
                                                                     using -20 & +5 as coefficients.
                                                                     Now, begin factoring inside the [ ]'s.

0.02[5sinx(10sinx + 1) - 2(10sinx + 1)]            ← Now, factor out (10sinx + 1)

       0.02[(5sinx - 2)(10sinx + 1)]

        0.02(5sinx - 2)(10sinx + 1)            ← ANSWER
                         OR
         ¹∕₅₀(5sinx - 2)(10sinx + 1)


Have a good one
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