Question

VWrite the cubic polynomial function f(x) in expanded form with zeros −6, −5, and −2, given that f(−1)=40

Answer 1

This is an interesting problem. The underlying solution is to solve a system of equations.

First we need to define what's a cubic polynomial function :

f(x) = $ax^{3}+bx^{2}+cx+d$, where a,b,c,d are constant values.

We assume from the problem that f(-1) = 40, and that the zeros of our unknown function are -6,-5 and -2.

This gives us a system of equation to solve :

$-216a +36b-6c+d=0\\-125a+25b-5c+d=0\\-8a+4b-2c+d=0\\-a+b-c+d = 40$

Good luck