Question

find the difference of the polynomials given below and classify it in terms of degree and number of terms.

\\3n^2(n^2 + 4n - 5) - (2n^2 - n^4 + 3)\\

\\(3^{\text{rd}}\\) degree polynomial with 5 terms

\\(4^{\text{th}}\\) degree polynomial with 5 terms

\\(4^{\text{th}}\\) degree polynomial with 4 terms

\\(3^{\text{rd}}\\) degree polynomial with 4 terms

Explanation:

Expand the first polynomial expression

$$ 3n^2(n^2 + 4n - 5) = 3n^4 + 12n^3 - 15n^2 $$

Subtract the second polynomial expression

$$
LATEXBLOCK0
$$

Classify the resulting polynomial

• The highest exponent is \(4\), so the degree is \(4\) (\(4^{\text{th}}\) degree).
• There are \(4\) distinct terms: \(4n^4\), \(12n^3\), \(-17n^2\), and \(-3\).

Answer:

• (A) \(3^{\text{rd}}\) degree polynomial with 5 terms
• (B) \(4^{\text{th}}\) degree polynomial with 5 terms
• (C) \(4^{\text{th}}\) degree polynomial with 4 terms (Correct answer)
• (D) \(3^{\text{rd}}\) degree polynomial with 4 terms