Question

Please help:) 100 points

Which of the following is equivalent to the statement “(–3, 0) is an x-intercept"?
1. –3 is a root.
2. –3 is a zero.
3. x + 3 is a factor.
4. All of the above are equivalent statements.

Answer 1

4. All of the above are equivalent statements.

Explanation:

The x-intercept is the point at which a line crosses the x-axis.

The roots of a function are the x-values of the x-intercepts.

Therefore, if (-3, 0) is an x-intercept, then -3 is a root.

The zeros of the function are the x-values when y = 0.

(-3, 0) means x = -3 when y = 0.

Therefore, -3 is a zero.

According to the factor theorem, if f(x) is a polynomial, and f(a) = 0, then (x – a) is a factor of f(x).

Given (-3, 0), then f(-3) = 0. Therefore, (x - (-3)) = (x + 3) is a factor.

Therefore, all given statements are equivalent statements.