# the constant differences of an 8 degree polynomial is 241920.What is the leading coefficient?

the constant differences of an 8 degree polynomial is 241920.What is the leading coefficient?
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Arham Warner

The relationship between the constant difference, d, the leading coefficient, c, and the degree, n, of a polynomial is $d=c\cdot n!$.
If the polynomial has a degree of $n=8$, a constant difference of $d=241,920$, and a leading coefficient of a, then $241,920=a\cdot 8!$.
The definition of a factorial is $n!=n\cdot \left(n-1\right)\cdot \left(n-2\right)\cdots \left(2\right)\left(1\right)$.

Using this definition gives $8!=8\left(7\right)\left(6\right)\left(5\right)\left(4\right)\left(3\right)\left(2\right)\left(1\right)$.

Using a calculator to evaluate the product then gives $8!=40,320$.
We then have $241,920=a\cdot 40,320$.
Dividing both sides by 40,320 then gives a leading coefficient of $a=\frac{241,920}{40,320}=6$