Recall the nested form for Newton's polynomial

$p(x)=a_0+(x-x_0)(a_1+(x-x_1)(a_2+(x-x_2)(a_3+$cdots$+a_n(x-x_{n-1}))))$

The following Matlab program computes the value of this polynomial:

function $p=$ nestedNewton $(a,xp,x)$

$//$ input: a $--$vector for a$\_n$ values,

$//xp--$ vector for $x_n$ values

$//x-.$ the point $x$ where $p(x)$ is evaluated

$//$ output: $p-.$ the value $p(x)$

$n=$lentgh$(a)$;$p=a(n)$;

for $k=n-1$:$-1$:$1$

$//$ missing content for the for$-10$op

end

end

Fill in the Matlab code that is missing in the for$-$loop.

$p=p^{**}(x-x(k))+a(k)$;

$p=p^{**}(x-x(k))-a(k)$;

$p=p^{**}(x^{**}x(k))+a(k)$;

$p=p(x-x(k))+a(k)$;