Chopping Up A Polynomial (2)

Algebra Level 2

If $x-1$ is a factor of the polynomial $a_nx^n+a_{n-1}x^{n-1}+...+a_1x+a_0$ then what is $\large\sum_{i=0}^{n} a_i?$

The answer is 0.

1 solution

Brian Moehring
Aug 8, 2018

Call the polynomial $P$ , so using function notation, $P(x) = \sum_{i=0}^n a_ix^i.$ Since $x-1$ is a factor of $P(x)$ , $\sum_{i=0}^n a_i = \sum_{i=0}^n a_i(1)^i = P(1) = \boxed{0}$

Chopping Up A Polynomial (2)

The answer is 0.

1 solution

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