Mister Exam
Other calculators
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How to use it?
- Factor squared:
- y^4+y^2-3
- y^4+y^2+4
- y^4-12*y^2+7
- y^2+4*y-3
- Factor polynomial:
- y^3+y^5
- x^3-x
- x1^2+x2^2
- x^3+7*x^2+15*x+9
- Least common denominator:
- (x*(x-6)^2)^(1/3)*((x-6)^2/3+x*(-12+2*x)/3)/(x*(x-6)^2)
- (2*a+b)/(a^2-b^2)+1/(a+b)
- (234/(((7/20)*p+1)*(p+1)*((111/10)*p+1)))*((3/10)+10/p)
- (z/(z-1))+((z^2-1.0923*z)/(z^2-1.9061*z+0.9277))
- How do you in partial fractions?:
- (x^2-x-6)/(x+2)
- (z-(5*z)/z+1)/(z-4)/(z+1)
- 1/(1+x^2/3)
- (x^2-5*x+6)/(x-3)
- Derivative of:
-
x^2-x+3
- Graphing y =:
- x^2-x+3
- Factor polynomial:
- x^2-x+3
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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,
$$\left(x - \frac{1}{2}\right)^{2} + \frac{11}{4}$$