Question

Write a polynomial function of the least degree with integral coefficients that has given zeros

Answer 1

y= 5x^3 + 14x^2 -23x + 4

which is the same as:

y=(5x-1)(x+4)(x-1) if your teacher wants it in factored form

Explanation:

y = (x - (1/5))(x+4)(x-1)

Let's clean up that first set of parentheses:

(x-(1/5)) =

x= 1/5

5x = 1

= (5x - 1)

so now the equation is:

y=(5x-1)(x+4)(x-1)

expand that, we'll do the first 2 terms first

(5x-1)(x+4)

= 5x^2+20x-1x-4 = 5x^2+19x-4

Now multiply that by (x-1)

(5x^2+19x-4) (x-1)

= 5x^3 - 5x^2+19x^2-19x-4x+4

combine like terms:

y= 5x^3+14x^2-23x+4