p = 0
Its degree is 0

p = 3.0
Its degree is 0

p = 2.5x^4 + 3.0
Its degree is 4

p = 2.5x^4 + -5.2x^3 + 3.0
Its degree is 4

The coefficient of power 800 is 0.0

The coefficient of power 10 is 0.0
The coefficient of power 9 is 0.0
The coefficient of power 8 is 0.0
The coefficient of power 7 is 0.0
The coefficient of power 6 is 0.0
The coefficient of power 5 is 0.0
The coefficient of power 4 is 2.5
The coefficient of power 3 is -5.2
The coefficient of power 2 is 0.0
The coefficient of power 1 is 0.0
The coefficient of power 0 is 3.0

p = 1.2x^1000 + -5.2x^3 + 3.0
Its degree is 1000

p = 1.2x^1000 + -5.2x^3 + 10.4x + 3.0
Its degree is 1000

p = 1.2x^1000 + -5.2x^3 + 3.0
Its degree is 1000

p = 1.2x^1000 + -1.0x^5 + -5.2x^3 + 3.0
Its degree is 1000

The value of p at 0 is 3.0
The value of p at 1.0 is -2.0
The value of p at 2.0 is 1.2858103286235207E301
The value of p at -15.6 is Infinity

q = p + p: 
q = 2.4x^1000 + -2.0x^5 + -10.4x^3 + 6.0

Change q and display it: 
q = 2.4x^1000 + -2.0x^5 + 6.0
q = 2.4x^1000 + -2.0x^5
q = 2.4x^1000
q = 2.4x^1000 + 8.7x^2
q = 2.4x^1000 + 5.0x^4 + 8.7x^2 + 1.0x + 2.0

r = p + q = 3.5999999999999996x^1000 + -1.0x^5 + 5.0x^4 + -5.2x^3 + 8.7x^2 + 1.0x + 5.0
where p = 1.2x^1000 + -1.0x^5 + -5.2x^3 + 3.0
  and q = 2.4x^1000 + 5.0x^4 + 8.7x^2 + 1.0x + 2.0

r = -3 * r = -10.799999999999999x^1000 + 3.0x^5 + -15.0x^4 + 15.600000000000001x^3 + -26.099999999999998x^2 + -3.0x + -15.0

r = 12.5 * r = -135.0x^1000 + 37.5x^5 + -187.5x^4 + 195.00000000000003x^3 + -326.25x^2 + -37.5x + -187.5

r = 0 * r = 0

r = s * t = 0
where s = 1.0x^2
  and t = 0

r = s * t = 1.0x^3
where s = 1.0x^2
  and t = 1.0x

r = t * t = 1.0x^2 + -2.0x + 1.0
where t = 1.0x + -1.0

r = s * t = 1.0x^3 + -1.0
where s = 1.0x^2 + 1.0x + 1.0
  and t = 1.0x + -1.0

r = s * s = 1.0x^4 + 2.0x^3 + 3.0x^2 + 2.0x + 1.0
where s = 1.0x^2 + 1.0x + 1.0

r = p * q = 2.88x^2000 + -2.4x^1005 + 6.0x^1004 + -12.48x^1003 + 8.04x^1002 + 1.2x^1001 + 9.6x^1000 + -5.0x^9 + -34.7x^7 + -6.0x^6 + -47.239999999999995x^5 + 1.1000000000000014x^4 + -11.4x^3 + 24.099999999999998x^2 + 3.0x + 6.0
where p = 1.2x^1000 + -1.0x^5 + -5.2x^3 + -1.0x^2 + 3.0
  and q = 2.4x^1000 + 5.0x^4 + 8.7x^2 + 1.0x + 2.0