A sequence has constant 3rd differences of 1. How many terms are in its standard form polynomial expression?

Answer 1

The 3rd difference of a polynomial sequence is constant and equal to 1. This means that the degree of the polynomial must be 3.

In general, a polynomial of degree $n$ can be expressed as $P(x)=a_nx^n+a_{n-1}x^{n-1}+\dots+a_1x+a_0$, where $n$ is a nonnegative integer.

Therefore, a polynomial of degree 3 would be expressed as $P(x)=a_3x^3+a_2x^2+a_1x+a_0$.

Since there are 4 different terms in the polynomial ($a_3x^3$, $a_2x^2$, $a_1x$, and $a_0$), the standard form polynomial expression has $\boxed{4}$ terms.