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 4 terms
\\(4^{\text{th}}\\) degree polynomial with 5 terms
\\(3^{\text{rd}}\\) degree polynomial with 5 terms
\\(4^{\text{th}}\\) 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

$$
LATEXBLOCK1
$$

Answer:

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