Question

Which of the following must be a factor of the function

Answer 1

(A) (x -2)

Explanation:

You want to know a factor of the function whose values given in the table include (x, y) = (2, 0).

Polynomial zeros

A polynomial function y = p(x) will have a factor of (x-a) if and only if p(a) = 0.

The table shows y=0 for x=2, so this polynomial function will have a factor of (x -2).

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Additional comment

The function shown in the table is ...

y = (x -2)²

so it actually has two factors that are (x -2).

You can tell this is a polynomial function of degree 2 because the 2nd differences are constant.

First differences between successive y-values: -7, -5, -3, -1, 1, 3

Second differences between successive first differences: 2, 2, 2, 2, 2.