The second degree polynomial with leading coefficient of -2 and root 4 with multiplicity of 2 is:
[tex]p(x) = -2*(x - 4)*(x - 4) = -2*(x - 4)^2[/tex]
A polynomial of degree N, with the N roots {x₁, ..., xₙ} and a leading coefficient a is written as:
[tex]p(x) = a*(x - x_1)*(x - x_2)*...*(x - x_n)[/tex]
Here we know that the degree is 2, the only root is 4 (with a multiplicity of 2, this is equivalent to say that we have two roots at x = 4) and a leading coefficient equal to -2.
Then this polynomial is equal to:
[tex]p(x) = -2*(x - 4)*(x - 4) = -2*(x - 4)^2[/tex]
If you want to learn more about polynomials:
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