Mister Exam
Other calculators
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How to use it?
- Factor squared:
- y^4+8*y^2+6
- -y^4+y^2+15
- y^4-8*y^2-2
- -y^4-y^2-1
- Factor polynomial:
- z^3+i
- z^3+9*z^2+25*z+17
- z^3-9*z^2+16*z+26
- z^3+8/125
- Least common denominator:
- y^2/((2-81)*y)-y/(y+9)
- ((x/(y-x))^-2)*((x^2+x*y)/(((x+y)^2)+4*x*y))
- a/(a+b)-a^2/(b^2-a^2)
- (z^2-2*t+2*t1+exp(t1/t)*(2*t-z^2))*(z^2-2*t+2*t2+exp(t2/t)*(2*t-z^2))
- How do you in partial fractions?:
- (x^2-6)/(x-3)-x/(x-3)
- (5*x^2-3*x-2)/(5*x^2+2*x)
- y/(y+2)+-y*(y+2)/(2-y)^2
- x^(2*n)/(x^n-1)^2
- Factor polynomial:
- x^2-x+1
- Derivative of:
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x^2-x+1
- Graphing y =:
- x^2-x+1
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Identical expressions
- x^ two -x+ one
- x squared minus x plus 1
- x to the power of two minus x plus one
- x2-x+1
- x²-x+1
- x to the power of 2-x+1
-
Similar expressions
- x^2+x+1
- x^2-x-1
Factor x^2-x+1 squared
The solution
The perfect square
Let's highlight the perfect square of the square three-member
$$\left(x^{2} - x\right) + 1$$
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
$$a = 1$$
$$b = -1$$
$$c = 1$$
Then
$$m = - \frac{1}{2}$$
$$n = \frac{3}{4}$$
So,
$$\left(x - \frac{1}{2}\right)^{2} + \frac{3}{4}$$
$$\left(x^{2} - x\right) + 1$$
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
$$a = 1$$
$$b = -1$$
$$c = 1$$
Then
$$m = - \frac{1}{2}$$
$$n = \frac{3}{4}$$
So,
$$\left(x - \frac{1}{2}\right)^{2} + \frac{3}{4}$$
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)