Determine whether g(x) = frac{x^3}{2} − x^2 + 2 is a polynomial. If it is, state its degree. If not, say why it is not a polynomial. If it is a polynomial, write it in standard form. Identify the leading term and the constant term.

vazelinahS 2021-02-03 Answered
Determine whether g(x)=x32x2+2 is a polynomial. If it is, state its degree. If not, say why it is not a polynomial. If it is a polynomial, write it in standard form. Identify the leading term and the constant term.
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Expert Answer

Demi-Leigh Barrera
Answered 2021-02-04 Author has 97 answers
Step 1
Given:
g(x)=x32x2+2
Step 2
Convert element to fracnion: x2=x222,2=2×22
=x32x2×22+2×22
Since the denominators are equal, combine the fractions: ac±bc=a±bc
=x3x2×2+2×22
Multiply the numbers: 2×2=4
g(x)=x32x2+42
Hence, it is a polynomial with its degree 3,
Step 3
Now, convert 3 degree polynomial into standard form which is
ax3+bx3+cx+d
Standard form g(x)=x322x2+0x+2
Leading term 12
Constant term 2

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Jeffrey Jordon
Answered 2022-07-06 Author has 2495 answers

Answer is given below (on video)

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