Mister Exam
Other calculators
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How to use it?
- Factor squared:
- y^4-9*y^2-2
- y^4-y^2+11
- -y^4+8*y^2+15
- y^4-8*y^2+12
- Factor polynomial:
- z^3-4*z^2+14*z-20
- z^3-3*z^2+4*z-2
- z^2-z+1
- z^2+2*z+10
- Least common denominator:
- (y/(x*y-x^2)+x/(x*y-y^2))/(x^2+2*x*y+y^2/(1/x+1/y))
- y-b/(a-a*b)-(y-a)/a*b-b
- y/(4*y+16)+(y^2+16)/(4*y^2-64)-(4/(y^2-4*y))
- y/(4*y+16)+y^2+16/(4*y^2-64)
- How do you in partial fractions?:
- -1/x+x/(2*x+3)
- (y/(x-y)+x/(x+y))/(1/x^2+1/y^2)-y^4/(x^2-y^2)
- -1/(10*tan(-1/2+5*x/2))+tan(-1/2+5*x/2)/10
- (y*x^2+16)/((y-1)*(x-4))-(16*y+x^2)/(x*y-x-4*y+4)
- Factor polynomial:
- x^2-x-1
- Graphing y =:
- 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 x^2-x-1 squared
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,
$$\left(x - \frac{1}{2}\right)^{2} - \frac{5}{4}$$