Mister Exam
Factor polynomial y^3+49+7+y^2
The solution
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3 2 y + 49 + 7 + y
$$y^{2} + \left(\left(y^{3} + 49\right) + 7\right)$$
y^3 + 49 + 7 + y^2
Factorization
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/ ___________________ / ___\\ / ___________________ / ___\\ | 3 / _______ | 1 I*\/ 3 || | 3 / _______ | 1 I*\/ 3 || / ___________________\ | \/ 757 + 6*\/ 15918 *|- - - -------|| | \/ 757 + 6*\/ 15918 *|- - + -------|| | 3 / _______ | | 1 1 \ 2 2 /| | 1 1 \ 2 2 /| | 1 1 \/ 757 + 6*\/ 15918 | |x + - + ---------------------------------------- + --------------------------------------|*|x + - + ---------------------------------------- + --------------------------------------|*|x + - + ------------------------ + ----------------------| | 3 ___________________ / ___\ 3 | | 3 ___________________ / ___\ 3 | | 3 ___________________ 3 | | 3 / _______ | 1 I*\/ 3 | | | 3 / _______ | 1 I*\/ 3 | | | 3 / _______ | | 3*\/ 757 + 6*\/ 15918 *|- - - -------| | | 3*\/ 757 + 6*\/ 15918 *|- - + -------| | \ 3*\/ 757 + 6*\/ 15918 / \ \ 2 2 / / \ \ 2 2 / /
$$\left(x + \left(\frac{1}{3} + \frac{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{6 \sqrt{15918} + 757}}{3} + \frac{1}{3 \left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{6 \sqrt{15918} + 757}}\right)\right) \left(x + \left(\frac{1}{3} + \frac{1}{3 \left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{6 \sqrt{15918} + 757}} + \frac{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{6 \sqrt{15918} + 757}}{3}\right)\right) \left(x + \left(\frac{1}{3 \sqrt[3]{6 \sqrt{15918} + 757}} + \frac{1}{3} + \frac{\sqrt[3]{6 \sqrt{15918} + 757}}{3}\right)\right)$$
((x + 1/3 + 1/(3*(757 + 6*sqrt(15918))^(1/3)*(-1/2 - i*sqrt(3)/2)) + (757 + 6*sqrt(15918))^(1/3)*(-1/2 - i*sqrt(3)/2)/3)*(x + 1/3 + 1/(3*(757 + 6*sqrt(15918))^(1/3)*(-1/2 + i*sqrt(3)/2)) + (757 + 6*sqrt(15918))^(1/3)*(-1/2 + i*sqrt(3)/2)/3))*(x + 1/3 + 1/(3*(757 + 6*sqrt(15918))^(1/3)) + (757 + 6*sqrt(15918))^(1/3)/3)