Question

Which polynomial could have the following graph?

Answer 1

ANSWER

y=(x+3)(x-1)(x-5)

EXPLANATION

The given polynomial has x-intercepts at x=-3,x=1,x=5

These are called the zeros of this polynomial.

We can use the factor theorem to obtain the polynomial in factored form.

The polynomial in factored form is of the form

y=a(x+3)(x-1)(x-5)

The polynomial rises on the left and keep rising on the right.

This implies that, the 'a' is positive.

Therefore

y=(x+3)(x-1)(x-5)

The correct choice is the first option.