Mister Exam
Other calculators
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How to use it?
- Factor polynomial:
- y^5+y^3+y^2+1
- a^2+8*a+16
- x^4-81
- y^2-81
- Least common denominator:
- k1/(1+k1*(-k2*k3*k3/((t3^2*s^2+2*t3*s*e+1)*(t2*s+1))+1/(t1*s+1)))
- factorial(n)/factorial(n+1)-(n-1)/factorial(n)
- (x1/3-y1/3)/(x+y)+1/(x2/3-x1/3*y1/3+y2/3)
- n*((1+p)^k+p^k*log(p)+(1+p)^k*(k+1)*log(1+p))/k-n*(p^k+(k+1)*(1+p)^k)/k^2
- Factor squared:
- -a^4-8*a^2-1
- -q^4-4*q^2+5
- -9*p^2-5*p-4
- 8*x^4-14*x^2-3
- How do you in partial fractions?:
- (6x^2+29x)/(x+5)
- 3*x^2/(8-x^4)+4*x^6/(8-x^4)^2
- (x^3+12*x)*(x/(2*(x^3+12*x))+(-12-3*x^2)*(x^2+4)/(4*(x^3+12*x)^2))/(x^2+4)
- 1/(n*(n+1)*(n+2))
-
Identical expressions
- -a^ four - eight *a^ two - one
- minus a to the power of 4 minus 8 multiply by a squared minus 1
- minus a to the power of four minus eight multiply by a to the power of two minus one
- -a4-8*a2-1
- -a⁴-8*a²-1
- -a to the power of 4-8*a to the power of 2-1
- -a^4-8a^2-1
- -a4-8a2-1
-
Similar expressions
- -a^4+8*a^2-1
- -a^4-8*a^2+1
- a^4-8*a^2-1
Factor -a^4-8*a^2-1 squared
The solution
The perfect square
Let's highlight the perfect square of the square three-member
$$\left(- a^{4} - 8 a^{2}\right) - 1$$
To do this, let's use the formula
$$a^{5} + a^{2} b + c = a \left(a^{2} + m\right)^{2} + n$$
where
$$m = \frac{b}{2 a}$$
$$n = \frac{4 a c - b^{2}}{4 a}$$
In this case
$$a = -1$$
$$b = -8$$
$$c = -1$$
Then
$$m = 4$$
$$n = 15$$
So,
$$-10$$
$$\left(- a^{4} - 8 a^{2}\right) - 1$$
To do this, let's use the formula
$$a^{5} + a^{2} b + c = a \left(a^{2} + m\right)^{2} + n$$
where
$$m = \frac{b}{2 a}$$
$$n = \frac{4 a c - b^{2}}{4 a}$$
In this case
$$a = -1$$
$$b = -8$$
$$c = -1$$
Then
$$m = 4$$
$$n = 15$$
So,
$$-10$$
Factorization
[src]
/ ____________\ / ____________\ / ____________\ / ____________\ | / ____ | | / ____ | | / ____ | | / ____ | \a + I*\/ 4 - \/ 15 /*\a - I*\/ 4 - \/ 15 /*\a + I*\/ 4 + \/ 15 /*\a - I*\/ 4 + \/ 15 /
$$\left(a - i \sqrt{4 - \sqrt{15}}\right) \left(a + i \sqrt{4 - \sqrt{15}}\right) \left(a + i \sqrt{\sqrt{15} + 4}\right) \left(a - i \sqrt{\sqrt{15} + 4}\right)$$
(((a + i*sqrt(4 - sqrt(15)))*(a - i*sqrt(4 - sqrt(15))))*(a + i*sqrt(4 + sqrt(15))))*(a - i*sqrt(4 + sqrt(15)))
Combining rational expressions
[src]
2 / 2\ -1 + a *\-8 - a /
$$a^{2} \left(- a^{2} - 8\right) - 1$$
-1 + a^2*(-8 - a^2)