How to Identify Polynomials in Standard Form

Which polynomials are in standard form? Check all that apply. The polynomials that are in standard form are:
  • 12x
  • 15x + 4

To determine which polynomials are in standard form, it's essential to understand what standard form means in the context of polynomials.

Polynomials:

A polynomial in mathematics is an expression made up of coefficients and indeterminates and involves only the operations of multiplication, addition, subtraction, and non-negative integer exponentiation of variables.

Standard Form:

In polynomial equations, standard form refers to the arrangement of terms based on the degree of the variables.

The highest degree of terms is written first, followed by the next degree, and so on, to represent a polynomial in standard form.

Given the polynomials provided:

  • 12x
  • 10x + 3x2 - 8
  • 15x + 4
  • 2-7x

From the options, polynomials (a) 12x and (c) 15x + 4 are in standard form, as they are arranged in descending order of degrees.

Polynomial (b) 10x + 3x2 - 8 is not in standard form as it has the terms arranged in non-standard order.

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