Polynomial Formulas

Question

Find a possible formula for a fourth degree polynomial g that has a double zero at 2, g(−6)=0,  g(6)=0, and g(0)=12.

Answer 1

g(x) = a(x - 2)²(x² - 36); g(0) = a(0 - 2)²(0 - 36) = 12; a = - 1/12.

So, g(x) = -1/12(x - 2)²(x² - 36)