Hello :
all n in N ; n(n+1)(n+2) = 3a a in N or : <span>≡ 0 (mod 3)
1 ) n </span><span>≡ 0 ( mod 3)...(1)
n+1 </span>≡ 1 ( mod 3)...(2)
n+2 ≡ 2 ( mod 3)...(3)
by (1), (2), (3) : n(n+1)(n+2) ≡ 0×1×2 ( mod 3) : ≡ 0 (mod 3)
2) n ≡ 1 ( mod 3)...(1)
n+1 ≡ 2 ( mod 3)...(2)
n+2 ≡ 3 ( mod 3)...(3)
by (1), (2), (3) : n(n+1)(n+2) ≡ 1×2 × 3 ( mod 3) : ≡ 0 (mod 3) , 6≡ 0 (mod)
3) n ≡ 2 ( mod 3)...(1)
n+1 ≡ 3 ( mod 3)...(2)
n+2 ≡ 4 ( mod 3)...(3)
by (1), (2), (3) : n(n+1)(n+2) ≡ 2×3 × 4 ( mod 3) : ≡ 0 (mod 3) , 24≡ 0 (mod3)
(8x^2+2x+8)+(3x^3+7x+4)=
8x^2+2x+8+3x^3+7x+4
3x^3+8x^2+(2+7)x+12=
3x^3+8x^2+9x+12
Answer: Option A. 3x^3+8x^2+9x+12
Answer:
Tina won 5 games more than maryann, and the sum of their games is 29.. 29-5/2= 12
Maryann won 12 games while Tina won 12+5= 17 games.
Answer:
The solutions are:

Step-by-step explanation:
We have the following quadratic equation

We can rewrite the equation as follows

Now we use the quadratic formula to solve the equation
For an equation of the form
the quadratic formula is:

In this case:

Then:




