Mister Exam
Other calculators
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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:
- factorial(n)/factorial(n+1)-(n-1)/factorial(n)
- a3*b3/a3-a2*b*b2-a2/4*ab2
- (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)
- Factor squared:
- -q^4-4*q^2+5
- -9*p^2-5*p-4
- x^2-x*a+4*a^2
- 8*x^4-14*x^2-3
- 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
- - nine *p^ two - five *p- four
- minus 9 multiply by p squared minus 5 multiply by p minus 4
- minus nine multiply by p to the power of two minus five multiply by p minus four
- -9*p2-5*p-4
- -9*p²-5*p-4
- -9*p to the power of 2-5*p-4
- -9p^2-5p-4
- -9p2-5p-4
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Similar expressions
- -9*p^2+5*p-4
- 9*p^2-5*p-4
- -9*p^2-5*p+4
Factor -9*p^2-5*p-4 squared
The solution
The perfect square
Let's highlight the perfect square of the square three-member
$$\left(- 9 p^{2} - 5 p\right) - 4$$
To do this, let's use the formula
$$a p^{2} + b p + c = a \left(m + p\right)^{2} + n$$
where
$$m = \frac{b}{2 a}$$
$$n = \frac{4 a c - b^{2}}{4 a}$$
In this case
$$a = -9$$
$$b = -5$$
$$c = -4$$
Then
$$m = \frac{5}{18}$$
$$n = - \frac{119}{36}$$
So,
$$- 9 \left(p + \frac{5}{18}\right)^{2} - \frac{119}{36}$$
$$\left(- 9 p^{2} - 5 p\right) - 4$$
To do this, let's use the formula
$$a p^{2} + b p + c = a \left(m + p\right)^{2} + n$$
where
$$m = \frac{b}{2 a}$$
$$n = \frac{4 a c - b^{2}}{4 a}$$
In this case
$$a = -9$$
$$b = -5$$
$$c = -4$$
Then
$$m = \frac{5}{18}$$
$$n = - \frac{119}{36}$$
So,
$$- 9 \left(p + \frac{5}{18}\right)^{2} - \frac{119}{36}$$
Factorization
[src]
/ _____\ / _____\ | 5 I*\/ 119 | | 5 I*\/ 119 | |p + -- + ---------|*|p + -- - ---------| \ 18 18 / \ 18 18 /
$$\left(p + \left(\frac{5}{18} - \frac{\sqrt{119} i}{18}\right)\right) \left(p + \left(\frac{5}{18} + \frac{\sqrt{119} i}{18}\right)\right)$$
(p + 5/18 + i*sqrt(119)/18)*(p + 5/18 - i*sqrt(119)/18)
Combining rational expressions
[src]
-4 + p*(-5 - 9*p)
$$p \left(- 9 p - 5\right) - 4$$
-4 + p*(-5 - 9*p)