Mister Exam
Other calculators
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How to use it?
- Factor polynomial:
- x^3-4*x
- m^2-n^2-m+n
- x^2-x^2
- x^2-x-1
- Least common denominator:
- (z^2-4*z+16)/(16*z^2-1)*(4*z^2+z)/(z^3+64)-(z+4)/(4*z^2-z)
- sqrt(m)/(m-16)-sqrt(m)/((4-sqrt(m))^2)
- z/t-t/z
- ((z+p)/(2*(z-p)))-((z-p)/(2*(z+p)))-((p)/(z-p))
- Factor squared:
- y^4-y^2+10
- y^4-y^2+1
- y^4-9*y^2+8
- y^4-y^2-1
- How do you in partial fractions?:
- ((z+2)/(2*z+4))+((2*z+1)/(3*z-4))
- -(z^2+1)/(z-(-1-sqrt(3)*i)/2)^2+2*z/(z-(-1-sqrt(3)*i)/2)
- 2*(-1+4*x^2/(1+x^2))/(1+x^2)^2
- 2*x/(x^2-1)
- Graphing y =:
- x^2-x-1
- Factor squared:
- x^2-x-1
- Integral of d{x}:
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x^2-x-1
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Identical expressions
- x^ two -x- one
- x squared minus x minus 1
- x to the power of two minus x minus one
- x2-x-1
- x²-x-1
- x to the power of 2-x-1
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Similar expressions
- x^2-x+1
- x^2+x-1
Factor polynomial x^2-x-1
The solution
Factorization
[src]
/ ___\ / ___\ | 1 \/ 5 | | 1 \/ 5 | |x + - - + -----|*|x + - - - -----| \ 2 2 / \ 2 2 /
$$\left(x + \left(- \frac{1}{2} + \frac{\sqrt{5}}{2}\right)\right) \left(x + \left(- \frac{\sqrt{5}}{2} - \frac{1}{2}\right)\right)$$
(x - 1/2 + sqrt(5)/2)*(x - 1/2 - sqrt(5)/2)
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
$$m = - \frac{1}{2}$$
$$n = - \frac{5}{4}$$
So,
$$\left(x - \frac{1}{2}\right)^{2} - \frac{5}{4}$$
$$\left(x^{2} - x\right) - 1$$
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
$$m = - \frac{1}{2}$$
$$n = - \frac{5}{4}$$
So,
$$\left(x - \frac{1}{2}\right)^{2} - \frac{5}{4}$$