Mister Exam
Factor polynomial a^7+a^4
The solution
Factorization
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/ ___\ / ___\
| 1 I*\/ 3 | | 1 I*\/ 3 |
(a + 1)*a*|a + - - + -------|*|a + - - - -------|
\ 2 2 / \ 2 2 /
$$a \left(a + 1\right) \left(a + \left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right)\right) \left(a + \left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right)\right)$$
(((a + 1)*a)*(a - 1/2 + i*sqrt(3)/2))*(a - 1/2 - i*sqrt(3)/2)
Combinatorics
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4 / 2 \ a *(1 + a)*\1 + a - a/
$$a^{4} \left(a + 1\right) \left(a^{2} - a + 1\right)$$
a^4*(1 + a)*(1 + a^2 - a)
Combining rational expressions
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4 / 3\ a *\1 + a /
$$a^{4} \left(a^{3} + 1\right)$$
a^4*(1 + a^3)