Question

How do you write the polynomial `a^3(a^2 + a + 1)` in standard form and how many terms and degree is it?

Answer 1

It is a polynomial of 5th degree. In standard form it is:

`a^5+a^4+a^3`

Explanation:

In such expression you have to multiply `a^3` by every term in the brackets, so:

`a^3*(a^2+a+1)=a^5+a^4+a^3`

To find the degree of a polynomial you look at the highest exponent to which `x` is raised and which has a non-zero coefficient. In this case the exponent is `5`, so the degree is also `5`. (If there is no coefficient, you treat such expression as if there was number `1` `a^5=1*a^5`)