Mister Exam
Other calculators
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How to use it?
- Factor polynomial:
- z^3+i
- z^3+9*z^2+25*z+17
- z^3-9*z^2+16*z+26
- z^3+8/125
- Least common denominator:
- y^2/((2-81)*y)-y/(y+9)
- ((x/(y-x))^-2)*((x^2+x*y)/(((x+y)^2)+4*x*y))
- a/(a+b)-a^2/(b^2-a^2)
- (z^2-2*t+2*t1+exp(t1/t)*(2*t-z^2))*(z^2-2*t+2*t2+exp(t2/t)*(2*t-z^2))
- Factor squared:
- y^4+8*y^2+6
- -y^4+y^2+15
- y^4-8*y^2-2
- -y^4-y^2-1
- How do you in partial fractions?:
- (x^2-6)/(x-3)-x/(x-3)
- (5*x^2-3*x-2)/(5*x^2+2*x)
- y/(y+2)+-y*(y+2)/(2-y)^2
- x^(2*n)/(x^n-1)^2
- Graphing y =:
- x^2-x-6
- Derivative of:
-
x^2-x-6
- Factor squared:
- x^2-x-6
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Identical expressions
- x^ two -x- six
- x squared minus x minus 6
- x to the power of two minus x minus six
- x2-x-6
- x²-x-6
- x to the power of 2-x-6
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Similar expressions
- x^2-x+6
- x^2+x-6
Factor polynomial x^2-x-6
The solution
The perfect square
Let's highlight the perfect square of the square three-member
$$\left(x^{2} - x\right) - 6$$
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,
$$\left(x - \frac{1}{2}\right)^{2} - \frac{25}{4}$$
$$\left(x^{2} - x\right) - 6$$
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,
$$\left(x - \frac{1}{2}\right)^{2} - \frac{25}{4}$$