Mister Exam
Factor polynomial 3*x^2+2*x-1
The solution
Factorization
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(x + 1)*(x - 1/3)
$$\left(x - \frac{1}{3}\right) \left(x + 1\right)$$
(x + 1)*(x - 1/3)
The perfect square
Let's highlight the perfect square of the square three-member
$$\left(3 x^{2} + 2 x\right) - 1$$
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
$$a = 3$$
$$b = 2$$
$$c = -1$$
Then
$$m = \frac{1}{3}$$
$$n = - \frac{4}{3}$$
So,
$$3 \left(x + \frac{1}{3}\right)^{2} - \frac{4}{3}$$
$$\left(3 x^{2} + 2 x\right) - 1$$
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
$$a = 3$$
$$b = 2$$
$$c = -1$$
Then
$$m = \frac{1}{3}$$
$$n = - \frac{4}{3}$$
So,
$$3 \left(x + \frac{1}{3}\right)^{2} - \frac{4}{3}$$
Combining rational expressions
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-1 + x*(2 + 3*x)
$$x \left(3 x + 2\right) - 1$$
-1 + x*(2 + 3*x)
Combinatorics
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(1 + x)*(-1 + 3*x)
$$\left(x + 1\right) \left(3 x - 1\right)$$
(1 + x)*(-1 + 3*x)