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

Sep 11, 2015

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:

${a}^{3} \cdot \left({a}^{2} + a + 1\right) = {a}^{5} + {a}^{4} + {a}^{3}$

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 $1$ ${a}^{5} = 1 \cdot {a}^{5}$)