Mister Exam
Other calculators
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How to use it?
- Factor polynomial:
- z^3-3*z^2+z+5
- z^3+3*z^2+4*z+12
- z^3+3*z^2+3*z+3
- z^3-2*z^2+z-2
- Least common denominator:
- (y/5*x-5*x-y)/(y+5*x)
- y^2/x^2+y/x
- ((y^2-49)/(y^2-14*y+49))^4/((y+7)/(y-7))^4
- x/y-y/x
- Factor squared:
- -y^4-7*y^2-7
- -y^4+7*y^2-4
- -y^4+7*y^2+4
- y^4-7*y^2+4
- How do you in partial fractions?:
- (x^2-3*x+2)/(x+4)
- (6/(a-1)-10/(a-1)^2)/(10/(a^2-1)-(2*a+2)/(a-1))
- -10-7*((x-2)/2-3/(x-2))+18/(x-2)^2+(x-2)^2/2
- (2*a^2)^3*(3*b)^2/(6*a^3*b)^2
- Derivative of:
-
z^2+z+1
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Identical expressions
- z^ two +z+ one
- z squared plus z plus 1
- z to the power of two plus z plus one
- z2+z+1
- z²+z+1
- z to the power of 2+z+1
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Similar expressions
- z^2+z-1
- z^2-z+1
Factor polynomial z^2+z+1
The solution
The perfect square
Let's highlight the perfect square of the square three-member
$$\left(z^{2} + z\right) + 1$$
To do this, let's use the formula
$$a z^{2} + b z + c = a \left(m + z\right)^{2} + n$$
where
$$m = \frac{b}{2 a}$$
$$n = \frac{4 a c - b^{2}}{4 a}$$
In this case
$$a = 1$$
$$b = 1$$
$$c = 1$$
Then
$$m = \frac{1}{2}$$
$$n = \frac{3}{4}$$
So,
$$\left(z + \frac{1}{2}\right)^{2} + \frac{3}{4}$$
$$\left(z^{2} + z\right) + 1$$
To do this, let's use the formula
$$a z^{2} + b z + c = a \left(m + z\right)^{2} + n$$
where
$$m = \frac{b}{2 a}$$
$$n = \frac{4 a c - b^{2}}{4 a}$$
In this case
$$a = 1$$
$$b = 1$$
$$c = 1$$
Then
$$m = \frac{1}{2}$$
$$n = \frac{3}{4}$$
So,
$$\left(z + \frac{1}{2}\right)^{2} + \frac{3}{4}$$
Factorization
[src]
/ ___\ / ___\ | 1 I*\/ 3 | | 1 I*\/ 3 | |x + - + -------|*|x + - - -------| \ 2 2 / \ 2 2 /
$$\left(x + \left(\frac{1}{2} - \frac{\sqrt{3} i}{2}\right)\right) \left(x + \left(\frac{1}{2} + \frac{\sqrt{3} i}{2}\right)\right)$$
(x + 1/2 + i*sqrt(3)/2)*(x + 1/2 - i*sqrt(3)/2)