Mister Exam
Other calculators
-
How to use it?
- Factor polynomial:
- x^4-81
- y^2-81
- u^2+2*u*v+v^2
- x^7+x^5+1
- Least common denominator:
- 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
- (k1*p*(k4*(t4*p+1))+k2/p)*k5*p+(k1*p)*(k3/(t3*p+1))
- a3*b3/a3-a2*b*b2-a2/4*ab2
- sin(2*pi+x)+((3*pi)/2-x)+cos(x+pi/2)
- Factor squared:
- -9*p^2-5*p-4
- 8*x^4-14*x^2-3
- x^2-x*a+4*a^2
- y^4-y^2-7
- How do you in partial fractions?:
- (x^2+2x-15)/(x+5)
- (((2s-2+2*s^2)/(-s*(2+s^2+2*s)))+((-2s^2+2s-6))/((s*(s^2+2*s+2))))*1/s-2/s
- (4x^2-3x+1)/(x^4+x^2)
- 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)
-
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
-
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)