$\mathrm{BernsteinBasis}\left(k,n,a,b,x\right)=\left(\genfrac{}{}{0ex}{}{n}{k}\right)\frac{{\left(b-x\right)}^{n-k}{\left(x-a\right)}^k}{{\left(b-a\right)}^n}$ defines the $k$th Bernstein polynomial of degree $n$ which is nonnegative on the interval $\left[a\,b\right]$.

At present, this can only be evaluated in Maple by prior use of the object-oriented representation obtained by P:=convert(p,MatrixPolynomialObject,x) and subsequent call to P:-Value(<x-value>), which uses the de Casteljau algorithm to evaluate the polynomial p.

$p≔3\mathrm{BernsteinBasis}\left(0\&comma;4\&comma;0\&comma;1\&comma;x\right)+5\mathrm{BernsteinBasis}\left(2\&comma;4\&comma;0\&comma;1\&comma;x\right)+7\mathrm{BernsteinBasis}\left(4\&comma;4\&comma;0\&comma;1\&comma;x\right)$

$p≔3\mathrm{BernsteinBasis}\left(0\&comma;4\&comma;0\&comma;1\&comma;x\right)+5\mathrm{BernsteinBasis}\left(2\&comma;4\&comma;0\&comma;1\&comma;x\right)+7\mathrm{BernsteinBasis}\left(4\&comma;4\&comma;0\&comma;1\&comma;x\right)$

$P≔\mathrm{convert}\left(p\&comma;\mathrm{MatrixPolynomialObject}\&comma;x\right)$

$P≔\mathrm{Record}\left(\mathrm{Value}={\mathrm{Default}}_{\mathrm{value}}\&comma;\mathrm{Variable}=x\&comma;\mathrm{Degree}=4\&comma;\mathrm{Coefficient}=\mathrm{coe}\&comma;\mathrm{Dimension}=\left[1\&comma;1\right]\&comma;\mathrm{Basis}=\mathrm{BernsteinBasis}\&comma;\mathrm{BasisParameters}=\left[4\&comma;0\&comma;1\right]\&comma;\mathrm{IsMonic}=\mathrm{mon}\&comma;\mathrm{OutputOptions}=\left[\mathrm{shape}=\left[\right]\&comma;\mathrm{storage}=\mathrm{rectangular}\&comma;\mathrm{order}=\mathrm{Fortran\_order}\&comma;\mathrm{fill}=0\&comma;\mathrm{attributes}=\left[\right]\right]\right)$

$P:-\mathrm{Degree}\left(\right)$

$4$

$P:-\mathrm{Value}\left(0\right)$

$\left[\begin{array}{c}3\end{array}\right]$

$P:-\mathrm{Value}\left(1\right)$

$\left[\begin{array}{c}7\end{array}\right]$

$P:-\mathrm{Value}\left(0.3\right)$

$\left[\begin{array}{c}2.100000000\end{array}\right]$

$\mathrm{factor}\left(P:-\mathrm{Value}\left(t\right)\left[1,1\right]\right)$

$40t^4-72t^3+48t^2-12t+3$