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Write the polynomial in standard form and classify it by degree and number of terms:

\[12x^2 - 4x^3 - 7x^2 + 6x - 2x^3\]

A) \(2x^3 - 5x^2 + 6x + 12\); degree 3, 4 terms

B) \(-4x^3 - 7x^2 + 6x - 2x^2 + 12\); degree 4, 5 terms

C) \(-6x^3 - 12x^2 + 6x + 12\); degree 3, 4 terms

D) \(4x^3 - 5x^2 + 6x - 12\); degree 3, 4 terms

1 Answer

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Final answer:

The polynomial is written in standard form as -6x^3 + 5x^2 + 6x, with a degree of 3 and consisting of 3 terms. No option provided matches this correct classification.

Step-by-step explanation:

To write the polynomial in standard form and classify it by degree and number of terms, we first need to combine like terms in the expression 12x2 - 4x3 - 7x2 + 6x - 2x3:

  • Combine like terms by adding coefficients of the same degree: -4x3 - 2x3 gives us -6x3, and 12x2 - 7x2 gives us 5x2.
  • After combining, the polynomial is -6x3 + 5x2 + 6x.
  • Put the terms in descending order of degree to get the standard form. As there are no other like terms to combine, the polynomial is already in standard form: -6x3 + 5x2 + 6x.

The polynomial has a highest degree of 3, which classifies it as a cubic polynomial. It consists of 3 terms.

Therefore, the correct classification for the polynomial is degree 3, 3 terms.

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