Mister Exam
Other calculators
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How to use it?
- Factor polynomial:
- x^6+x^8-x^3+4*x
- x^6-x^5
- x^6-x^2+4*x
- x+6-x^2
- Least common denominator:
- tan((3*pi/2)-a)*sin(pi-a)*cos((3*pi/2)+a)+cos(2*a)*sin(pi-2*a)
- sqrt((x+4)/(1-x))+x*sqrt((x+4)/(1-x))*(1-x)*(1/(2*(1-x))+(x+4)/(2*(1-x)^2))/(x+4)
- sqrt(x^3/(x-6))*(x-6)*(-x^3/(2*(x-6)^2)+3*x^2/(2*(x-6)))/x^3
- sqrt(x^3*cos(x))*(-x^3*sin(x)/2+3*x^2*cos(x)/2)/(x^3*cos(x))
- Factor squared:
- -y^2+8*y*x-8*x^2
- y^2-9*y+8
- -y^2-8*y*b+9*b^2
- y^2-8*y*x-4*x^2
- How do you in partial fractions?:
- sqrt(x^2+4)*(1/(sqrt(x^2+4))-x^2/(x^2+4)^(3/2))/x
- (sqrt(pi)*erf(sqrt(2)*x+5/sqrt(2)))/(2*sqrt(pi))
- sqrt(b^2*((1-(b^2-a^2)/(b^2+a^2))^2+(2*a-b*sqrt(1-((b-a)*(b+a)/(b^2+a^2))^2)^2)))
- sqrt(10)/(100*(1+x^2/10))
- Integral of d{x}:
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x+6-x^2
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Identical expressions
- x+ six -x^ two
- x plus 6 minus x squared
- x plus six minus x to the power of two
- x+6-x2
- x+6-x²
- x+6-x to the power of 2
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Similar expressions
- x+6+x^2
- x-6-x^2
Factor polynomial x+6-x^2
The solution
The perfect square
Let's highlight the perfect square of the square three-member
$$- x^{2} + \left(x + 6\right)$$
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
$$a = -1$$
$$b = 1$$
$$c = 6$$
Then
$$m = - \frac{1}{2}$$
$$n = \frac{25}{4}$$
So,
$$\frac{25}{4} - \left(x - \frac{1}{2}\right)^{2}$$
$$- x^{2} + \left(x + 6\right)$$
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
$$a = -1$$
$$b = 1$$
$$c = 6$$
Then
$$m = - \frac{1}{2}$$
$$n = \frac{25}{4}$$
So,
$$\frac{25}{4} - \left(x - \frac{1}{2}\right)^{2}$$