Mister Exam
Other calculators
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How to use it?
- Factor polynomial:
- x^8-4
- y^5-32
- c^3-d^3
- x^8-y^8
- Least common denominator:
- x^4/4+x+2+x^4/4+x+2
- (x*(x-1)^2)^(1/3)*((x-1)^2/3+x*(-2+2*x)/3)/(x*(x-1)^2)
- ((x*x-11*x+30)/(x*x-9*x+20))/((x*x-36)/(x*x-16))
- ((x^-6-64)/(4+2*x^-1+x^-2))*(x^2/(4-4/x+1/x^2))-(4*x^2*(2*x+1))/(1-2*x)
- Factor squared:
- x^2-x-2
- -y^2-4*y-3
- -8*p^2+6*p+1
- x^2+x-6
- How do you in partial fractions?:
- (5*a^2+3*a-2)/(a^2-1)
- ((2*x+10)/(3*x))/(2*x^2+20*x+50*x)
- y/(b*y-2*b^2)-2/(y^2+y-2*b*y-2*b)*(1+(3*y+y^2)/(3+y))
- (u^2-4*u+16)/(16*u^2-1)*(4*u^2+u)/(u^3+64)
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Identical expressions
- - eight *p^ two + six *p+ one
- minus 8 multiply by p squared plus 6 multiply by p plus 1
- minus eight multiply by p to the power of two plus six multiply by p plus one
- -8*p2+6*p+1
- -8*p²+6*p+1
- -8*p to the power of 2+6*p+1
- -8p^2+6p+1
- -8p2+6p+1
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Similar expressions
- 8*p^2+6*p+1
- -8*p^2+6*p-1
- -8*p^2-6*p+1
Factor -8*p^2+6*p+1 squared
The solution
The perfect square
Let's highlight the perfect square of the square three-member
$$\left(- 8 p^{2} + 6 p\right) + 1$$
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
$$a = -8$$
$$b = 6$$
$$c = 1$$
Then
$$m = - \frac{3}{8}$$
$$n = \frac{17}{8}$$
So,
$$\frac{17}{8} - 8 \left(p - \frac{3}{8}\right)^{2}$$
$$\left(- 8 p^{2} + 6 p\right) + 1$$
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
$$a = -8$$
$$b = 6$$
$$c = 1$$
Then
$$m = - \frac{3}{8}$$
$$n = \frac{17}{8}$$
So,
$$\frac{17}{8} - 8 \left(p - \frac{3}{8}\right)^{2}$$
Factorization
[src]
/ ____\ / ____\ | 3 \/ 17 | | 3 \/ 17 | |p + - - + ------|*|p + - - - ------| \ 8 8 / \ 8 8 /
$$\left(p + \left(- \frac{3}{8} + \frac{\sqrt{17}}{8}\right)\right) \left(p + \left(- \frac{\sqrt{17}}{8} - \frac{3}{8}\right)\right)$$
(p - 3/8 + sqrt(17)/8)*(p - 3/8 - sqrt(17)/8)
Combining rational expressions
[src]
1 + 2*p*(3 - 4*p)
$$2 p \left(3 - 4 p\right) + 1$$
1 + 2*p*(3 - 4*p)