Mister Exam
Other calculators
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How to use it?
- Factor polynomial:
- x^2+y^2
- x^7+1
- x^2+1^2
- x^2-x+1
- Least common denominator:
- (((z)/(b))-((b)/(z)))*((4*z*b)/(z+b))
- z-8/z^2/3*z^(1/3)+4
- (z/3)+(54-z-z/3)+z
- (z^2-4*z+16)/(16*z^2-1)*(4*z^2+z)/(z^3+64)-(z+4)/(4*z^2-z)/7/(z^2+4*z)-(20*z+13)/(7-28*z)
- Factor squared:
- -y^4+y^2+1
- -y^4-9*y^2+7
- y^4+9*y^2-6
- y^4-y^2-10
- How do you in partial fractions?:
- x^3*y^12/(x*y^4)^3
- -16/(x-3)+(x^2+7)/(x-3)
- (((y-y)/(3*y-3))+(1/(y-1)))/((y+1)/3)+(2/(y^2-1))
- y/(y+3)^2-y/(y^2)-9
- Derivative of:
-
x^2-x+1
- Graphing y =:
- x^2-x+1
- Integral of d{x}:
- x^2-x+1
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Identical expressions
- x^ two -x+ one
- x squared minus x plus 1
- x to the power of two minus x plus one
- x2-x+1
- x²-x+1
- x to the power of 2-x+1
-
Similar expressions
- x^2+x+1
- x^2-x-1
Factor polynomial x^2-x+1
The solution
The perfect square
Let's highlight the perfect square of the square three-member
$$\left(x^{2} - x\right) + 1$$
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
$$a = 1$$
$$b = -1$$
$$c = 1$$
Then
$$m = - \frac{1}{2}$$
$$n = \frac{3}{4}$$
So,
$$\left(x - \frac{1}{2}\right)^{2} + \frac{3}{4}$$
$$\left(x^{2} - x\right) + 1$$
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
$$a = 1$$
$$b = -1$$
$$c = 1$$
Then
$$m = - \frac{1}{2}$$
$$n = \frac{3}{4}$$
So,
$$\left(x - \frac{1}{2}\right)^{2} + \frac{3}{4}$$
Factorization
[src]
/ ___\ / ___\ | 1 I*\/ 3 | | 1 I*\/ 3 | |x + - - + -------|*|x + - - - -------| \ 2 2 / \ 2 2 /
$$\left(x + \left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right)\right) \left(x + \left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right)\right)$$
(x - 1/2 + i*sqrt(3)/2)*(x - 1/2 - i*sqrt(3)/2)