Question

Use the description below to write the formula (in factored form) for a polynomial of least degree. If you have a non-integer coefficient then write it as a fraction.

Organize factors (left to right) from smallest zero to largest.

Description:
The degree of the polynomial is 3. Zeros at x=-2, x=1, and x=3. Y-intercept at (0,-4).

Thanks! :D

Answer 1

Answer: f(x) = (-2/3)(x + 2)(x - 1)(x - 3)

Explanation:

To find the polynomial of least degree with the given zeros and y-intercept, we use the factored form of a polynomial. For a polynomial of degree 3, the factored form is:

f(x) = a(x - r1)(x - r2)(x - r3)

where a is the leading coefficient and r1, r2, and r3 are the zeros of the polynomial.

Given zeros at x = -2, x = 1, and x = 3, we can write the factored form as:

f(x) = a(x + 2)(x - 1)(x - 3)

Now, we need to find the value of the leading coefficient, a. To do that, we use the y-intercept, which is given as (0, -4). Since the y-intercept is a point on the graph of the polynomial, we can substitute x = 0 and y = -4 into the factored form:

-4 = a(0 + 2)(0 - 1)(0 - 3)

Simplify:

-4 = a(2)(-1)(-3)

-4 = 6a

Now, solve for a:

a = -4/6

a = -2/3

Finally, we have the factored form of the polynomial:

f(x) = (-2/3)(x + 2)(x - 1)(x - 3)