Mister Exam
Other calculators
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How to use it?
- Factor polynomial:
- x*y+y^2*x/8
- x-y+y^2
- x*y*x-x*y
- x-y*x^3/3
- Least common denominator:
- x^2*y+16/(y-1)*(x-4)-16*y+x^2/x*y-x-4*y+4
- x/2-sin(2*(x/2+1))/2+1
- (x-2*cos(x)/sin(x)+2*x*cos(x)^2/sin(x)^2)/sin(x)
- x^2-91/10-3*x*2/(x-4)-4*x*(-1)/((x^2-x-12)*(x+3))
- Factor squared:
- y^4+12*y^2+12
- -y^2+y-5
- -y^2-y-4
- -y^2+y-4
- How do you in partial fractions?:
- (4x-1)/(x^2-4x+8)
- x/(x^4-1)
- x/(x+1)^3
- (x+8)/x^2+16*x+64/(x-8)
- Factor squared:
- x^2-x+3
- Derivative of:
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x^2-x+3
- Graphing y =:
- 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
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Similar expressions
- x^2+x+3
- x^2-x-3
Factor polynomial x^2-x+3
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,
$$\left(x - \frac{1}{2}\right)^{2} + \frac{11}{4}$$