Mister Exam
Factor polynomial x^2-14*x+33
The solution
The perfect square
Let's highlight the perfect square of the square three-member
$$\left(x^{2} - 14 x\right) + 33$$
To do this, let's use the formula
$$a x^{2} + b x + c = a \left(m + x\right)^{2} + n$$
where
$$m = \frac{b}{2 a}$$
$$n = \frac{4 a c - b^{2}}{4 a}$$
In this case
$$a = 1$$
$$b = -14$$
$$c = 33$$
Then
$$m = -7$$
$$n = -16$$
So,
$$\left(x - 7\right)^{2} - 16$$
$$\left(x^{2} - 14 x\right) + 33$$
To do this, let's use the formula
$$a x^{2} + b x + c = a \left(m + x\right)^{2} + n$$
where
$$m = \frac{b}{2 a}$$
$$n = \frac{4 a c - b^{2}}{4 a}$$
In this case
$$a = 1$$
$$b = -14$$
$$c = 33$$
Then
$$m = -7$$
$$n = -16$$
So,
$$\left(x - 7\right)^{2} - 16$$
Combining rational expressions
[src]
33 + x*(-14 + x)
$$x \left(x - 14\right) + 33$$
33 + x*(-14 + x)
Combinatorics
[src]
(-11 + x)*(-3 + x)
$$\left(x - 11\right) \left(x - 3\right)$$
(-11 + x)*(-3 + x)