Mister Exam
Other calculators
-
How to use it?
- Factor squared:
- y^4-y^2+3
- y^4-y^2+12
- -y^4-y^2+15
- -y^4-y^2-11
- Factor polynomial:
- x^3-8
- x^2+x-6
- x^10-1
- m^2-n^2-m+n
- Least common denominator:
- (z/(z-1))+((z^2-1.0923*z)/(z^2-1.9061*z+0.9277))
- (z/x-z+x+z/z)/x/x^2-x*z^2
- z/(x+y)+x/(z+y)+y/(z+x)
- (z/x*x-3*x)/(z*z/3*x-9)
- How do you in partial fractions?:
- (z-2)/(6*z+(z-2)*(z-2))+(6/(z*z*z-8))
- 2*(-1+(-1+x)/(2+x))/(2+x)^2
- (x+5)/(x^2+22*x+85)
- 5*((x-4)/(x^2+4*x)-16/(16-x^2))/(1+4/x)
- Derivative of:
-
x^2-x+3
- Graphing y =:
- x^2-x+3
- Factor polynomial:
- x^2-x+3
-
Identical expressions
- x^ two -x+ three
- x squared minus x plus 3
- x to the power of two minus x plus three
- x2-x+3
- x²-x+3
- x to the power of 2-x+3
-
Similar expressions
- x^2+x+3
- x^2-x-3
Factor x^2-x+3 squared
The solution
Factorization
[src]
/ ____\ / ____\ | 1 I*\/ 11 | | 1 I*\/ 11 | |x + - - + --------|*|x + - - - --------| \ 2 2 / \ 2 2 /
$$\left(x + \left(- \frac{1}{2} - \frac{\sqrt{11} i}{2}\right)\right) \left(x + \left(- \frac{1}{2} + \frac{\sqrt{11} i}{2}\right)\right)$$
(x - 1/2 + i*sqrt(11)/2)*(x - 1/2 - i*sqrt(11)/2)
The perfect square
Let's highlight the perfect square of the square three-member
$$\left(x^{2} - x\right) + 3$$
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
$$a = 1$$
$$b = -1$$
$$c = 3$$
Then
$$m = - \frac{1}{2}$$
$$n = \frac{11}{4}$$
So,
$$\left(x - \frac{1}{2}\right)^{2} + \frac{11}{4}$$
$$\left(x^{2} - x\right) + 3$$
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
$$a = 1$$
$$b = -1$$
$$c = 3$$
Then
$$m = - \frac{1}{2}$$
$$n = \frac{11}{4}$$
So,
$$\left(x - \frac{1}{2}\right)^{2} + \frac{11}{4}$$