Question

How do you write \[2{{x}^{5}}-12+3x\] in standard form?

Answer 1

Hint:In the given question, you have been asked to write a polynomial in a standard form. To write a polynomial in standard form, you need to carefully examine the degree of each term given in a polynomial. Then you need to write each term in the order of decreasing degree i.e. from the highest to the lowest and from left to the right.

Complete step by step answer:
We have given a polynomial that is,
\[2{{x}^{5}}-12+3x\]
Classify the term with the highest degree in the given polynomial \[2{{x}^{5}}-12+3x\] is \[2{{x}^{5}}\].
Start writing the polynomial with the term with the highest degree,
\[2{{x}^{5}}-12+3x\]
Again classify or examine the term with the degree less than the term with the highest degree in the given polynomial. Write each term in the order of decreasing degree i.e. from the highest to the lowest and from left to the right,
\[2{{x}^{5}}+3x-12\]
Since \[2{{x}^{5}}\] term is the term with the highest degree in the given polynomial, we then write the term with the degree lower than the term with the highest degree i.e. \[3x\] and lastly end with the constant term i.e. 12.

Thus, we get the given polynomial in the standard form as: \[ 2{{x}^{5}}+3x-12\].

Note:In mathematics, the degree of a term in a polynomial is the highest degree of each individual term in the given polynomial with non-zero coefficients. Standard form of a polynomial refers to the fact that you write each term of the given polynomial by decreasing degree and end the polynomial only by constant term.