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)

Tahmid Knox

Tahmid Knox

Answered question

2021-05-25

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(x3)2(x2+5)

Answer & Explanation

lobeflepnoumni

lobeflepnoumni

Skilled2021-05-26Added 99 answers

Step 1
The given function is:
G(x)=2(x3)2(x2+5)
Step 2
Therefore:
G(x)=2(x26x+9)(x2+5)
G(x)=2(x46x3+14x230x+45)
G(x)=2x412x3+28x260x+90
Hence the given function is a polynomial of degree 4.
The standard form of the polynomial is:
G(x)=2x412x3+28x260x+90
Leading term : 2
Constant term : 90

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