An Orthonormal Basis for $P_3$

Question

I am currently taking a linear algebra course and we are using the textbook by Larson, 7th edition. On page 249, the text says that

In $P_3$, with the inner product $$\langle p,q\rangle = a_0b_0 + a_1b_1 + a_2b_2 + a_3b_3$$ the standard basis $B = \{1,x,x^2,x^3\}$ is orthonormal.

The book gives that the the magnitude (the length) of the every element in $B$ is $1$. My question is: how did they find that?

Answer 1

The magnitude of an element $p$ is $\sqrt{\langle p, p \rangle}$. Apply this to each element of $B$.