Mister Exam
Factor -y^4-4*y^2-6 squared
The solution
The perfect square
Let's highlight the perfect square of the square three-member
$$\left(- y^{4} - 4 y^{2}\right) - 6$$
To do this, let's use the formula
$$a y^{4} + b y^{2} + c = a \left(m + y^{2}\right)^{2} + n$$
where
$$m = \frac{b}{2 a}$$
$$n = \frac{4 a c - b^{2}}{4 a}$$
In this case
$$a = -1$$
$$b = -4$$
$$c = -6$$
Then
$$m = 2$$
$$n = -2$$
So,
$$- \left(y^{2} + 2\right)^{2} - 2$$
$$\left(- y^{4} - 4 y^{2}\right) - 6$$
To do this, let's use the formula
$$a y^{4} + b y^{2} + c = a \left(m + y^{2}\right)^{2} + n$$
where
$$m = \frac{b}{2 a}$$
$$n = \frac{4 a c - b^{2}}{4 a}$$
In this case
$$a = -1$$
$$b = -4$$
$$c = -6$$
Then
$$m = 2$$
$$n = -2$$
So,
$$- \left(y^{2} + 2\right)^{2} - 2$$
Factorization
[src]
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$$\left(x + \left(\sqrt[4]{6} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{2}}{2} \right)}}{2} \right)} - \sqrt[4]{6} i \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{2}}{2} \right)}}{2} \right)}\right)\right) \left(x + \left(\sqrt[4]{6} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{2}}{2} \right)}}{2} \right)} + \sqrt[4]{6} i \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{2}}{2} \right)}}{2} \right)}\right)\right) \left(x + \left(- \sqrt[4]{6} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{2}}{2} \right)}}{2} \right)} + \sqrt[4]{6} i \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{2}}{2} \right)}}{2} \right)}\right)\right) \left(x + \left(- \sqrt[4]{6} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{2}}{2} \right)}}{2} \right)} - \sqrt[4]{6} i \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{2}}{2} \right)}}{2} \right)}\right)\right)$$
(((x + 6^(1/4)*sin(atan(sqrt(2)/2)/2) + i*6^(1/4)*cos(atan(sqrt(2)/2)/2))*(x + 6^(1/4)*sin(atan(sqrt(2)/2)/2) - i*6^(1/4)*cos(atan(sqrt(2)/2)/2)))*(x - 6^(1/4)*sin(atan(sqrt(2)/2)/2) + i*6^(1/4)*cos(atan(sqrt(2)/2)/2)))*(x - 6^(1/4)*sin(atan(sqrt(2)/2)/2) - i*6^(1/4)*cos(atan(sqrt(2)/2)/2))
Combining rational expressions
[src]
2 / 2\ -6 + y *\-4 - y /
$$y^{2} \left(- y^{2} - 4\right) - 6$$
-6 + y^2*(-4 - y^2)