How do you write a polynomial in standard form, then classify it by degree and number of terms 4x2−3x3+6x+7?

1 Answer
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Mar 6, 2016

The expression in standard form is −3x3+4x2+6x+7.

There are 4 non-zero terms.

The degree is 3.

Explanation:

There are 4 terms. They are

  1. −3x3.
  2. 4x2.
  3. 6x.
  4. 7.

A polynomial in standard form should meet the following criteria:

  • It should be expressed as a sum of, powers of x (or any other variable used).

For example, this is in standard form

x2−4x+3,

not

(x−1)⋅(x−3),

nor

(x−2)2−1.

  • The term with the highest power goes first.

For example, this is in standard form

x2−4x+3,

not

3−4x+x2.

The polynomial 4x2−3x3+6x+7 is not in standard form, as the term −3x3 comes after the term 4x2. Exchanging the two terms will solve the problem. So it becomes −3x3+4x2+6x+7.

The degree of polynomial is the highest power throughout the polynomial.

Since the powers are in decreasing order for a polynomial, the degree would be the power of the first term, which is a.k.a. the leading term.

The first term is −3x3. The degree is 3.

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