Mister Exam
Other calculators
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How to use it?
- Factor polynomial:
- -y^2+y^2/2
- -y^2-y^2
- y^2+y^2
- y^2-x*y+x-3*y+2
- Least common denominator:
- ((x^3+6*x^2+11*x+6)/(-6))+((-x^3-9*x^2-26*x-24)/6)
- (((x^3-64)*(x-7))/((x+7)*(x^2+4*x+16)))-((77-11*x)/(x+7))
- x^2*y+16/(y-1)*(x-4)-16*y+x^2/x*y-x-4*y+4
- x/2+x/4+x/8
- Factor squared:
- y^4+2*y^2+1
- -y^4-15*y^2-8
- y^4+2*y^2-7
- y^4-2*y^2-15
- How do you in partial fractions?:
- x^2-9/(x+3)^2
- (4x^2-19x+12)/(x^3-64)
- 1/(x^4+x^2)
- (C^2-5c)/(c^2-25)
- Derivative of:
-
x^2-x+3
- Factor squared:
- 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,
$$\left(x - \frac{1}{2}\right)^{2} + \frac{11}{4}$$