Mister Exam
Other calculators
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How to use it?
- Factor polynomial:
- x^3-8
- m^2-n^2-m+n
- x^8+1
- x^2-x-4
- Least common denominator:
- z/(x+y)+x/(z+y)+y/(z+x)
- (z/t-t/z)*5*t*z/z-t
- pi*sin(pi/(z+1))/(z+1)^2
- cos(p-2)*tan(2*p+2)/cos(3*p/2+2)
- Factor squared:
- y^4-y^2+3
- -y^4-y^2+15
- y^4-y^2-9
- x^2-x-3
- How do you in partial fractions?:
- (x^2-8*x+16)/(x-4)
- 1/(x+2)^2
- 2*(-1+(-1+x)/(2+x))/(2+x)^2
- (x+5)/(x^2+22*x+85)
- Factor squared:
- x^2-x+2
- Equation:
- x^2-x+2
- Derivative of:
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x^2-x+2
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Identical expressions
- x^ two -x+ two
- x squared minus x plus 2
- x to the power of two minus x plus two
- x2-x+2
- x²-x+2
- x to the power of 2-x+2
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Similar expressions
- x^2+x+2
- x^2-x-2
Factor polynomial x^2-x+2
The solution
Factorization
[src]
/ ___\ / ___\ | 1 I*\/ 7 | | 1 I*\/ 7 | |x + - - + -------|*|x + - - - -------| \ 2 2 / \ 2 2 /
$$\left(x + \left(- \frac{1}{2} - \frac{\sqrt{7} i}{2}\right)\right) \left(x + \left(- \frac{1}{2} + \frac{\sqrt{7} i}{2}\right)\right)$$
(x - 1/2 + i*sqrt(7)/2)*(x - 1/2 - i*sqrt(7)/2)
The perfect square
Let's highlight the perfect square of the square three-member
$$\left(x^{2} - x\right) + 2$$
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
$$a = 1$$
$$b = -1$$
$$c = 2$$
Then
$$m = - \frac{1}{2}$$
$$n = \frac{7}{4}$$
So,
$$\left(x - \frac{1}{2}\right)^{2} + \frac{7}{4}$$
$$\left(x^{2} - x\right) + 2$$
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
$$a = 1$$
$$b = -1$$
$$c = 2$$
Then
$$m = - \frac{1}{2}$$
$$n = \frac{7}{4}$$
So,
$$\left(x - \frac{1}{2}\right)^{2} + \frac{7}{4}$$