SOLUTION
According to this topic, we know it is a polynomial with 3 degrees, and it has three zeros which are
[tex]x=-2,-2,3[/tex]
and it passes through (0,-3).
Therefore, we suppose its equation is:
[tex]f(x)=a(x+2)(x+2)(x-3)=a(x+2)^2(x-3)[/tex]
Then (0,-3) is located in f(x).
Hence, let us solve for the value of 'a' if the y-intercept is (0,-3).
[tex]\begin{gathered} \text{when, x = 0, y = -3} \\ f(0)=-3 \\ \therefore-3=a(0+2)(0+2)(0-3) \\ -3=a(2)(2)(-3)=-12a \\ -3=-12a \\ a=\frac{-3}{-12}=\frac{1}{4} \\ \therefore a=\frac{1}{4} \end{gathered}[/tex]
Therefore, the formula for the polynomial function of least degree is
[tex]f(x)=\frac{1}{4}(x+2)^2(x-3)[/tex]
