Write polynomial

Question

write a polynomial f(x) that meets the given conditions.

 

Degree 3 polynomial with leading coefficient of 1 and zeros of 3, -5 and 4  

Answer 1

With zeros of 3, -5 and 4, we know that the factors of this polynomial are (x-3)(x+5) and (x-4).

 

(x-3)(x+5)(x-4) = (x² +2x - 15)(x-4) = (x³ + 2x² - 15x - 4x² - 8x + 60)

 

Combine like terms

x³ - 2x² - 23x + 60

 

The above polynomial satisfies the conditions.  It has an x³ term which means it's a 3rd degree polynomial and the coefficient of x³ is 1. 

 

Hope this helps.