Mister Exam
Other calculators
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How to use it?
- Factor squared:
- y^4+y^2-1
- y^4+9*y^2-3
- y^4+9*y^2+3
- y^4+9*y^2+2
- Factor polynomial:
- x^3-1
- x^7+1
- x^2-x+1
- m^2-n^2+m+n
- Least common denominator:
- z^(((p-3)/(p^2+3*p))/(12/(9-p^2))*(3/(3*p-p^2)))
- (z/c+c/z)/(z^2+c^2)/(5*z^9*c)
- (z/c-c/z)*5*z*c/(z+c)
- (z/b-b/z)*6*z*b/(z+b)
- How do you in partial fractions?:
- (((z^2)+(6*z+4))/((z^3)+8))/(1/-1)
- (a^2+a*b)/(a+b)
- x^3*y^12/(x*y^4)^3
- (x^2+x-6)/(x+2)
- Derivative of:
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x^4-5*x^2+4
- Graphing y =:
- x^4-5*x^2+4
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Identical expressions
- x^ four - five *x^ two + four
- x to the power of 4 minus 5 multiply by x squared plus 4
- x to the power of four minus five multiply by x to the power of two plus four
- x4-5*x2+4
- x⁴-5*x²+4
- x to the power of 4-5*x to the power of 2+4
- x^4-5x^2+4
- x4-5x2+4
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Similar expressions
- x^4-5*x^2-4
- x^4+5*x^2+4
Factor x^4-5*x^2+4 squared
The solution
Factorization
[src]
(x + 2)*(x + 1)*(x - 1)*(x - 2)
$$\left(x + 1\right) \left(x + 2\right) \left(x - 1\right) \left(x - 2\right)$$
(((x + 2)*(x + 1))*(x - 1))*(x - 2)
The perfect square
Let's highlight the perfect square of the square three-member
$$\left(x^{4} - 5 x^{2}\right) + 4$$
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
$$a = 1$$
$$b = -5$$
$$c = 4$$
Then
$$m = - \frac{5}{2}$$
$$n = - \frac{9}{4}$$
So,
$$\left(x^{2} - \frac{5}{2}\right)^{2} - \frac{9}{4}$$
$$\left(x^{4} - 5 x^{2}\right) + 4$$
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
$$a = 1$$
$$b = -5$$
$$c = 4$$
Then
$$m = - \frac{5}{2}$$
$$n = - \frac{9}{4}$$
So,
$$\left(x^{2} - \frac{5}{2}\right)^{2} - \frac{9}{4}$$
Combinatorics
[src]
(1 + x)*(-1 + x)*(-2 + x)*(2 + x)
$$\left(x - 2\right) \left(x - 1\right) \left(x + 1\right) \left(x + 2\right)$$
(1 + x)*(-1 + x)*(-2 + x)*(2 + x)
Combining rational expressions
[src]
2 / 2\ 4 + x *\-5 + x /
$$x^{2} \left(x^{2} - 5\right) + 4$$
4 + x^2*(-5 + x^2)