find a degree 3 polynomial having zeros

Question

 Find a degree 3 polynomial having zeros -3, 3 and 6 and the coefficient of X³ equal 1.

The polynomial is?

 

Answer 1

Hi Dalia,

 

By the factor theorem, the required polynomial have factors (x-3),(x+3) and (x-6)

 

therefore the solution is P(x)= (x-3)(x+3)(x-6)

 

                                         =(x²-9)(x-6)

 

                                         =x²(x-6)-9(x-6)

 

                                         =x³-6x²-9x+54

Answer 2

p(x) = 1(x- -3)(x-3)(x-6)

 

p(x) = (x+3)(x-3)(x-6)

 

p(x) = (x^2-9)(x-6)

 

p(x) = x^2(x-6)-9(x-6)

 

p(x) = x^3-6x^2-9x+54