Mister Exam
Factor polynomial y^3-5*y^2-2*y+16
The solution
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3 2 y - 5*y - 2*y + 16
$$\left(- 2 y + \left(y^{3} - 5 y^{2}\right)\right) + 16$$
y^3 - 5*y^2 - 2*y + 16
Factorization
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/ ____\ / ____\
| 3 \/ 41 | | 3 \/ 41 |
(x - 2)*|x + - - + ------|*|x + - - - ------|
\ 2 2 / \ 2 2 /
$$\left(x - 2\right) \left(x + \left(- \frac{3}{2} + \frac{\sqrt{41}}{2}\right)\right) \left(x + \left(- \frac{\sqrt{41}}{2} - \frac{3}{2}\right)\right)$$
((x - 2)*(x - 3/2 + sqrt(41)/2))*(x - 3/2 - sqrt(41)/2)
General simplification
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3 2 16 + y - 5*y - 2*y
$$y^{3} - 5 y^{2} - 2 y + 16$$
16 + y^3 - 5*y^2 - 2*y
Common denominator
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3 2 16 + y - 5*y - 2*y
$$y^{3} - 5 y^{2} - 2 y + 16$$
16 + y^3 - 5*y^2 - 2*y
Trigonometric part
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3 2 16 + y - 5*y - 2*y
$$y^{3} - 5 y^{2} - 2 y + 16$$
16 + y^3 - 5*y^2 - 2*y
Combining rational expressions
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16 + y*(-2 + y*(-5 + y))
$$y \left(y \left(y - 5\right) - 2\right) + 16$$
16 + y*(-2 + y*(-5 + y))
Combinatorics
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/ 2 \ (-2 + y)*\-8 + y - 3*y/
$$\left(y - 2\right) \left(y^{2} - 3 y - 8\right)$$
(-2 + y)*(-8 + y^2 - 3*y)
Rational denominator
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3 2 16 + y - 5*y - 2*y
$$y^{3} - 5 y^{2} - 2 y + 16$$
16 + y^3 - 5*y^2 - 2*y
Assemble expression
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3 2 16 + y - 5*y - 2*y
$$y^{3} - 5 y^{2} - 2 y + 16$$
16 + y^3 - 5*y^2 - 2*y