Mister Exam
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How to use it?
- Factor polynomial:
- x^6*y^9-64*x^3
- y^5+y^3+y^2+1
- x^7+x^5+1
- m^3+m^2+m+1-m^4-m^3-m^2-m-1
- Least common denominator:
- (x-1)*(1/(2*(x-1))-(x+1)/(2*(x-1)^2))/(x+1)
- sin(2*pi+x)+((3*pi)/2-x)+cos(x+pi/2)
- ((x*x^(1/2)-x)^3)/((((x^(3/4)-1)/(x^(1/4)-1)-x^(1/2))*(1-x))^3)
- cos(a)/2*sin(2)-1-sin(a)/2*cos(2)-1
- Factor squared:
- x^2-x*a+4*a^2
- 8*x^4-14*x^2-3
- 5*p^4-3*p^2+13
- 2*p^4+p^2-2
- How do you in partial fractions?:
- (x^2+2x-15)/(x+5)
- (4x^2-3x+1)/(x^4+x^2)
- ((p+3)/(p^2-2p))*((4p-8)/(p+3))
- a^3-a^2-a-2/(a^3+1)*a^3-2*a^2+2*a-1/(a^3+a^2+a)*a^2+a/(a^2-3*a+2)
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Identical expressions
- eight *x^ four - fourteen *x^ two - three
- 8 multiply by x to the power of 4 minus 14 multiply by x squared minus 3
- eight multiply by x to the power of four minus fourteen multiply by x to the power of two minus three
- 8*x4-14*x2-3
- 8*x⁴-14*x²-3
- 8*x to the power of 4-14*x to the power of 2-3
- 8x^4-14x^2-3
- 8x4-14x2-3
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Similar expressions
- 8*x^4-14*x^2+3
- 8*x^4+14*x^2-3
Factor 8*x^4-14*x^2-3 squared
The solution
You have entered
[src]
4 2 8*x - 14*x - 3
$$\left(8 x^{4} - 14 x^{2}\right) - 3$$
8*x^4 - 14*x^2 - 3
The perfect square
Let's highlight the perfect square of the square three-member
$$\left(8 x^{4} - 14 x^{2}\right) - 3$$
To do this, let's use the formula
$$a x^{4} + b x^{2} + c = a \left(m + x^{2}\right)^{2} + n$$
where
$$m = \frac{b}{2 a}$$
$$n = \frac{4 a c - b^{2}}{4 a}$$
In this case
$$a = 8$$
$$b = -14$$
$$c = -3$$
Then
$$m = - \frac{7}{8}$$
$$n = - \frac{73}{8}$$
So,
$$8 \left(x^{2} - \frac{7}{8}\right)^{2} - \frac{73}{8}$$
$$\left(8 x^{4} - 14 x^{2}\right) - 3$$
To do this, let's use the formula
$$a x^{4} + b x^{2} + c = a \left(m + x^{2}\right)^{2} + n$$
where
$$m = \frac{b}{2 a}$$
$$n = \frac{4 a c - b^{2}}{4 a}$$
In this case
$$a = 8$$
$$b = -14$$
$$c = -3$$
Then
$$m = - \frac{7}{8}$$
$$n = - \frac{73}{8}$$
So,
$$8 \left(x^{2} - \frac{7}{8}\right)^{2} - \frac{73}{8}$$
Factorization
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/ ______________\ / ______________\ / ____________\ / ____________\ | / ____ | | / ____ | | / ____ | | / ____ | | / 7 \/ 73 | | / 7 \/ 73 | | / 7 \/ 73 | | / 7 \/ 73 | |x + I* / - - + ------ |*|x - I* / - - + ------ |*|x + / - + ------ |*|x - / - + ------ | \ \/ 8 8 / \ \/ 8 8 / \ \/ 8 8 / \ \/ 8 8 /
$$\left(x - i \sqrt{- \frac{7}{8} + \frac{\sqrt{73}}{8}}\right) \left(x + i \sqrt{- \frac{7}{8} + \frac{\sqrt{73}}{8}}\right) \left(x + \sqrt{\frac{7}{8} + \frac{\sqrt{73}}{8}}\right) \left(x - \sqrt{\frac{7}{8} + \frac{\sqrt{73}}{8}}\right)$$
(((x + i*sqrt(-7/8 + sqrt(73)/8))*(x - i*sqrt(-7/8 + sqrt(73)/8)))*(x + sqrt(7/8 + sqrt(73)/8)))*(x - sqrt(7/8 + sqrt(73)/8))
Combining rational expressions
[src]
2 / 2\ -3 + 2*x *\-7 + 4*x /
$$2 x^{2} \left(4 x^{2} - 7\right) - 3$$
-3 + 2*x^2*(-7 + 4*x^2)