Consider the polynomial 2x^{3}-3x^{2}+x^{5}. Which of the following statements about the polynomial are not correct? A. The standard form of the polynomial is x^{5}+2x^{3}-3x^{2}. B. The polynomial is a trinomial. C. The polynomial is quintic. D. The polynomial has a linear term.

generals336 2021-08-08 Answered
Consider the polynomial \(\displaystyle{2}{x}^{{{3}}}-{3}{x}^{{{2}}}+{x}^{{{5}}}\). Which of the following statements about the polynomial are not correct?
A. The standard form of the polynomial is \(\displaystyle{x}^{{{5}}}+{2}{x}^{{{3}}}-{3}{x}^{{{2}}}\).
B. The polynomial is a trinomial.
C. The polynomial is quintic.
D. The polynomial has a linear term.

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Expert Answer

Demi-Leigh Barrera
Answered 2021-08-09 Author has 15692 answers
Step 1 A. Standard form of polynomial-
Standard form of polynomial is written with highest degree term as first term, second highest degree term as second term and so on.
For the given polynomial, the standard form is-
\(\displaystyle{x}^{{{5}}}+{2}{x}^{{{3}}}-{3}{x}^{{{2}}}\)
Step 2 B. Check whether correct or not-
Trinomial is a type of polynomial which has 3 terms.
The given polynomial is a trinomial as it has 3 terms, i.e.,
\(\displaystyle{x}^{{{5}}}-{1}-{s}{t}\) term
\(\displaystyle{2}{x}^{{{3}}}-{2}-{n}{d}\) term
\(\displaystyle{3}{x}^{{{2}}}-{3}-{r}{d}\) term
Step 3 C. Quintic polynomial-
The polynomials having degree 5th are known as quintic polynomials.
Since, the polynomial \(\displaystyle{x}^{{{5}}}+{2}{x}^{{{3}}}-{3}{x}^{{{2}}}\) have degree \(\displaystyle={5}\)
Hence, it is quintic polynomial.
Step 4 D. Linear term-
Linear term is term which have degree \(\displaystyle={1}\).
Since, the polynomial \(\displaystyle{x}^{{{5}}}+{2}{x}^{{{3}}}-{3}{x}^{{{2}}}\) has no term having 5th degree, hence the statement is not correct.
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