Mister Exam
Factor polynomial y^2+y-6
The solution
The perfect square
Let's highlight the perfect square of the square three-member
$$\left(y^{2} + y\right) - 6$$
To do this, let's use the formula
$$a y^{2} + b y + c = a \left(m + y\right)^{2} + n$$
where
$$m = \frac{b}{2 a}$$
$$n = \frac{4 a c - b^{2}}{4 a}$$
In this case
$$a = 1$$
$$b = 1$$
$$c = -6$$
Then
$$m = \frac{1}{2}$$
$$n = - \frac{25}{4}$$
So,
$$\left(y + \frac{1}{2}\right)^{2} - \frac{25}{4}$$
$$\left(y^{2} + y\right) - 6$$
To do this, let's use the formula
$$a y^{2} + b y + c = a \left(m + y\right)^{2} + n$$
where
$$m = \frac{b}{2 a}$$
$$n = \frac{4 a c - b^{2}}{4 a}$$
In this case
$$a = 1$$
$$b = 1$$
$$c = -6$$
Then
$$m = \frac{1}{2}$$
$$n = - \frac{25}{4}$$
So,
$$\left(y + \frac{1}{2}\right)^{2} - \frac{25}{4}$$