Mister Exam
Factor polynomial t-7-t^2
The solution
The perfect square
Let's highlight the perfect square of the square three-member
$$- t^{2} + \left(t - 7\right)$$
To do this, let's use the formula
$$a t^{2} + b t + c = a \left(m + t\right)^{2} + n$$
where
$$m = \frac{b}{2 a}$$
$$n = \frac{4 a c - b^{2}}{4 a}$$
In this case
$$a = -1$$
$$b = 1$$
$$c = -7$$
Then
$$m = - \frac{1}{2}$$
$$n = - \frac{27}{4}$$
So,
$$- \left(t - \frac{1}{2}\right)^{2} - \frac{27}{4}$$
$$- t^{2} + \left(t - 7\right)$$
To do this, let's use the formula
$$a t^{2} + b t + c = a \left(m + t\right)^{2} + n$$
where
$$m = \frac{b}{2 a}$$
$$n = \frac{4 a c - b^{2}}{4 a}$$
In this case
$$a = -1$$
$$b = 1$$
$$c = -7$$
Then
$$m = - \frac{1}{2}$$
$$n = - \frac{27}{4}$$
So,
$$- \left(t - \frac{1}{2}\right)^{2} - \frac{27}{4}$$
Factorization
[src]
/ ___\ / ___\ | 1 3*I*\/ 3 | | 1 3*I*\/ 3 | |t + - - + ---------|*|t + - - - ---------| \ 2 2 / \ 2 2 /
$$\left(t + \left(- \frac{1}{2} - \frac{3 \sqrt{3} i}{2}\right)\right) \left(t + \left(- \frac{1}{2} + \frac{3 \sqrt{3} i}{2}\right)\right)$$
(t - 1/2 + 3*i*sqrt(3)/2)*(t - 1/2 - 3*i*sqrt(3)/2)