Step 1

The given function is:

\(G(x)=2(x-3)^{2}(x^{2}+5)\)

Step 2

Therefore:

\(G(x)=2(x^{2}-6x+9)(x^{2}+5)\)

\(G(x)=2(x^{4}-6x^{3}+14x^{2}-30x+45)\)

\(G(x)=2x^{4}-12x^{3}+28x^{2}-60x+90\)

Hence the given function is a polynomial of degree 4.

The standard form of the polynomial is:

\(G(x)=2x^{4}-12x^{3}+28x^{2}-60x+90\)

Leading term : 2

Constant term : 90

The given function is:

\(G(x)=2(x-3)^{2}(x^{2}+5)\)

Step 2

Therefore:

\(G(x)=2(x^{2}-6x+9)(x^{2}+5)\)

\(G(x)=2(x^{4}-6x^{3}+14x^{2}-30x+45)\)

\(G(x)=2x^{4}-12x^{3}+28x^{2}-60x+90\)

Hence the given function is a polynomial of degree 4.

The standard form of the polynomial is:

\(G(x)=2x^{4}-12x^{3}+28x^{2}-60x+90\)

Leading term : 2

Constant term : 90