Mister Exam
Other calculators
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How to use it?
- Factor squared:
- y^4-y^2+15
- y^4+y^2+4
- -y^4+y^2+11
- y^4-y^2-5
- Factor polynomial:
- x^3+27
- x+x^2
- x^6-729
- x^5+y^5+z^5
- Least common denominator:
- -2*sqrt(3)/(3*sqrt(1-(2*x-1)^2/3))
- (2*a+b)/(a^2-b^2)+1/(a+b)
- z*((-z)*log(x)/c+z*log(y)/c)
- (z*z-1/2*z)/(z*z-z+1)*z/(z-1/2)
- How do you in partial fractions?:
- (z/c+c/z)/((z^2+c^2)/(5*z^9*c))
- (z-3)/(z+3)*(z+(z^2)/(3-z))
- (y^2-16)/(4*y^2-y^3)
- y/(y+2)+(1/(4-y^2)-1/(4-4*y+y^2))/(2/(y-2)^2)
- Graphing y =:
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x^2+x-3
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Identical expressions
- x^ two +x- three
- x squared plus x minus 3
- x to the power of two plus x minus three
- x2+x-3
- x²+x-3
- x to the power of 2+x-3
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Similar expressions
- x^2+x+3
- x^2-x-3
Factor x^2+x-3 squared
The solution
The perfect square
Let's highlight the perfect square of the square three-member
$$\left(x^{2} + x\right) - 3$$
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
$$a = 1$$
$$b = 1$$
$$c = -3$$
Then
$$m = \frac{1}{2}$$
$$n = - \frac{13}{4}$$
So,
$$\left(x + \frac{1}{2}\right)^{2} - \frac{13}{4}$$
$$\left(x^{2} + x\right) - 3$$
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
$$a = 1$$
$$b = 1$$
$$c = -3$$
Then
$$m = \frac{1}{2}$$
$$n = - \frac{13}{4}$$
So,
$$\left(x + \frac{1}{2}\right)^{2} - \frac{13}{4}$$
Factorization
[src]
/ ____\ / ____\ | 1 \/ 13 | | 1 \/ 13 | |x + - - ------|*|x + - + ------| \ 2 2 / \ 2 2 /
$$\left(x + \left(\frac{1}{2} - \frac{\sqrt{13}}{2}\right)\right) \left(x + \left(\frac{1}{2} + \frac{\sqrt{13}}{2}\right)\right)$$
(x + 1/2 - sqrt(13)/2)*(x + 1/2 + sqrt(13)/2)