Mister Exam
Other calculators
-
How to use it?
- Factor polynomial:
- z^3+3*z^2+4*z+12-0
- z^3+11*z^2+36*z+26
- z^2-a/z-z
- z^2+9*z+27+27/z
- Least common denominator:
- (y/5*x-5*x-y)/(y+5*x)
- x/y-y/x
- ((x/(y-x))^(-2)-((x+y)^(2)-4*x*y)/(x^(2)-x*y))^(2)*(x^4)/(x^(2)*y^(2)-y^4)
- ((x*y)+sin(x))/(|1-y|*(log(x)/log(10)))
- Factor squared:
- -y^4-8*y^2-1
- -y^4+7*y^2+11
- -y^4-7*y^2-1
- -y^4-6*y^2+8
- How do you in partial fractions?:
- (x^2-4*x+3)/(x+2)
- ((x+1)/(2x-3))+((x-1)/(2x+3))-((2x^2-7x)/(4x^2-9))
- x^3/(x^4-1)
- sqrt(1-((1-x*x)*(n0*n0)/(n1*n1)))
- Graphing y =:
- x^2+x-1
- Integral of d{x}:
-
x^2+x-1
- Canonical form:
- x^2+x-1
-
Identical expressions
- x^ two +x- one
- x squared plus x minus 1
- x to the power of two plus x minus 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 polynomial x^2+x-1
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
$$m = \frac{1}{2}$$
$$n = - \frac{5}{4}$$
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,
$$\left(x + \frac{1}{2}\right)^{2} - \frac{5}{4}$$
Factorization
[src]
/ ___\ / ___\ | 1 \/ 5 | | 1 \/ 5 | |x + - - -----|*|x + - + -----| \ 2 2 / \ 2 2 /
$$\left(x + \left(\frac{1}{2} - \frac{\sqrt{5}}{2}\right)\right) \left(x + \left(\frac{1}{2} + \frac{\sqrt{5}}{2}\right)\right)$$
(x + 1/2 - sqrt(5)/2)*(x + 1/2 + sqrt(5)/2)