Question

# Determine whether the following function is a polynomial function. If the function is a polynomial​ function, state its degree. If not why? Write the polynomial in standard form. Then identify the leading term and the constant term. G(x)=2(x-3)^{2}(x^{2}+5)

Polynomial factorization
Determine whether the following function is a polynomial function. If the function is a polynomial​ function, state its degree. If not why? Write the polynomial in standard form. Then identify the leading term and the constant term.
$$G(x)=2(x-3)^{2}(x^{2}+5)$$

2021-05-26
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:
$$G(x)=2x^{4}-12x^{3}+28x^{2}-60x+90$$