Mister Exam
Other calculators
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How to use it?
- Factor squared:
- y^4-y^2-3
- x^2+x-2
- y^2-4*y+3
- x^2+x-3
- Factor polynomial:
- x^4+1
- x^3-1^3+3^3-x^3
- y^2/2+y^23/23
- -x^7+x^6/4+9*x*5/8-9*x^4/32-x^3/8+x^2/32
- Least common denominator:
- (a+1/a+2)/a+1
- 1/(1+x^2/3)
- (z/x-z+x+z/z)/x/x^2-z^2
- (z/x-z+x+z/z)/x/x^2-x*z^2
- How do you in partial fractions?:
- z-2/4*z^2+16*z+16/(z/2*z-4-z^2+4/2*z^2-8-2/z^2+2*z)
- sqrt(b)-(b-1/b^2)/(sqrt(b)-1/sqrt(b))+(1-1/b^2)/(sqrt(b)+1/sqrt(b))+2/b^(3/2)
- sqrt((625*x^4+25*10^10*x^2)/(1+25*x^2))
- 3/(x^3+5)-9*x^3/(x^3+5)^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)