Finding Zeros and X-Intercepts (factored form)

The zeros of a polynomial are the values of x that make the polynomial equal to zero.

An x-intercept is a point where the graph of a function crosses the x-axis, meaning the output (y-value) is zero.

Set each factor equal to zero and solve for x.

The factored form is typically written as $$a(x - r_1)(x - r_2)$$ , where r_1 and r_2 are the roots.

The x-intercepts are $$x = -5$$ and $$x = -1$$ .

The solutions are $$x = 3$$ and $$x = -6$$ .

Factor to get $$n(n + 3) = 0$$ , leading to solutions $$n = 0$$ and $$n = -3$$ .

The solutions indicate the points where the graph intersects the x-axis.

A polynomial of degree n can have up to n real zeros.

Repeated factors indicate that the corresponding zero has a multiplicity greater than one.