Different way of expressing the interpolation error

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So I have got the problem about another way of expressing the interpolating error. And unfortunately I am clueless.

The question is that I should show that it is possible to Express the representation error as $f(x)-p_{n}(x)=f[x_{0},...,x_{n},x]\omega_{n}(x)$

In this case $\omega_{n}(t)= \prod\limits_{k=0}^n x = (t-x_{k})$

What I am supposed to know is the interpolation error theorem, and newtons representation. I was given the proofs for these theorems, which confused me a lot. Somehow I should prove the above with help from these known theorems, but unfortunately I have no idea.