Mister Exam
Other calculators
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How to use it?
- Factor polynomial:
- x^2+3
- x^4-x
- x*y^3-x^3*y^2
- x^2-1
- Least common denominator:
- 4*x^(3/2)/3+2*sqrt(x)+x^5/5+e^(5*x^3+1)/15
- z*((-z)*log(x)/c+z*log(y)/c)
- (z*z-1/2*z)/(z*z-z+1)*z/(z-1/2)
- -x^2/(x-2)^2+2*x/(x-2)
- Factor squared:
- y^4+y^2+2
- y^4+y^2-15
- y^4-y^2-5
- -y^4+8*y^2-8
- How do you in partial fractions?:
- (z^2-4*z+16)/(16*z^2-1)*(4*z^2+z)/(z^3+64)-(z+4)/(4*z^2-z)
- (5x^2+9x-2)/(x^2-5x-14)
- y/(y+2)+(1/(4-y^2)-1/(4-4*y+y^2))/(2/(y-2)^2)
- 1/(2*sqrt(x))
- Derivative of:
-
x^2+x+2
- Canonical form:
- x^2+x+2
- Factor squared:
- x^2+x+2
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Identical expressions
- x^ two +x+ two
- x squared plus x plus 2
- x to the power of two plus x plus two
- x2+x+2
- x²+x+2
- x to the power of 2+x+2
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Similar expressions
- x^2-x+2
- x^2+x-2
Factor polynomial x^2+x+2
The solution
Factorization
[src]
/ ___\ / ___\ | 1 I*\/ 7 | | 1 I*\/ 7 | |x + - + -------|*|x + - - -------| \ 2 2 / \ 2 2 /
$$\left(x + \left(\frac{1}{2} - \frac{\sqrt{7} i}{2}\right)\right) \left(x + \left(\frac{1}{2} + \frac{\sqrt{7} i}{2}\right)\right)$$
(x + 1/2 + i*sqrt(7)/2)*(x + 1/2 - i*sqrt(7)/2)
The perfect square
Let's highlight the perfect square of the square three-member
$$\left(x^{2} + x\right) + 2$$
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
$$a = 1$$
$$b = 1$$
$$c = 2$$
Then
$$m = \frac{1}{2}$$
$$n = \frac{7}{4}$$
So,
$$\left(x + \frac{1}{2}\right)^{2} + \frac{7}{4}$$
$$\left(x^{2} + x\right) + 2$$
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
$$a = 1$$
$$b = 1$$
$$c = 2$$
Then
$$m = \frac{1}{2}$$
$$n = \frac{7}{4}$$
So,
$$\left(x + \frac{1}{2}\right)^{2} + \frac{7}{4}$$