Mister Exam
Other calculators
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How to use it?
- Factor polynomial:
- z^3-2*z^2+2*z-1
- z^3-19*z^2/10-z/5+1/10
- z^2-z+5
- z^2+z-4
- Least common denominator:
- (y/5*x-5*x-y)/(y+5*x)
- y/(4*y+16)+(y^2+16)/(4*y^2-64)-(4/(y^2-4*y))
- ((y^2-49)/(y^2-14*y+49))^4/((y+7)/(y-7))^4
- x/y-y/x
- Factor squared:
- -y^4+9*y^2-13
- -y^4-7*y^2-11
- y^4+7*y^2-10
- -y^4-8*y^2-3
- How do you in partial fractions?:
- (9-m^2)/(m^2+3*m)
- -2/(x*x^2)
- tan(x+pi/8)/2-1/(2*tan(x+pi/8))
- (a^2+4*a)/(a^2+8*a+16)
- Graphing y =:
- x^2+x-1
- Integral of d{x}:
-
x^2+x-1
- Canonical form:
- x^2+x-1
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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)