Question

Write a polynomial function of least degree with zeroes

–

1, 5,9

Write your answer using the variable x and in standard form with a leading coefficient of 1

Answer 1

So a function with the zeroes 1, 5, 9 has to have a form of the expressions (x-1)(x-5)(x-9). But because it’s standard form, we have to multiply those together to create a polynomial.
By multiplying together (x-1) and (x-5) we get x^2 - 5x - 1x + 5, which simplifies to x^2 - 6x + 5.
Now we have to add (x-9). When we multiply that with the polynomial we just got, we get x^3 - 6x^2 + 5x - 9x^2 + 54x - 45, which simplifies to x^3 - 15x^2 + 59x - 45.
So the function is y = x^3 - 15x^2 + 59x - 45