Math Polynomial Equations

Question

Write a polynomial function of least degree that has rational coefficients, a leading coefficient of 1, and the given intercepts.

-1, 2, 3

Answer 1

Recall that if a polynomial equation can be factored into the form

0= (x-a)(x-b)(x-c), the intercepts will be at the x values of a, b and c.

You have been asked to do the reverse. Given intercepts of -1, 2 and 3, let a= -1, let b=2 and let c=3.

Plug into the above equation to get

0= (x+1)(x-2)(x-3)

Note that for three x intercepts, the minimum degree of the polynomial will be 3. There are no extra or duplicated roots in the above.

Multiply this out to get the final answer

f(x)= x^3 - 4x^2 + x + 6