Polynomial help

Question

Find a degree 3 polynomial function having zeros 2, -8 and -3 and leading coefficient 6.

The polynomial is     



(Give your answer as a function, with y as the output. You do not need to simplify your answer.)

Answer 1

f(x)=y = 6(x-2)(x+8)(x+3)

y = 6(x-2)(x^2 +11x+24)

y = 6(x^3 +11x^2 +24x -2x^2 -22x -48)

y = 6(x^3 +9x^2 +2x -48)

y =6x^3 +54x^2 +12x -288

is the polynomial with leading coefficient 6, zeros 2, -8 and -3

f(2) = 6(8)+54(4) +12(2) -288

= 48+216+24-288 = 288-288=0

f(-8)=0= f(-3)=f(2)