Question

find the sum and classify the polynomial based on degree and number of terms.
\\3n^2(5n^2 - 2n + 1) + (4n^2 - 11n^4 - 9)\\

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

Explanation:

Distribute and expand the terms

$$ 3n^2(5n^2 - 2n + 1) + (4n^2 - 11n^4 - 9) = 15n^4 - 6n^3 + 3n^2 + 4n^2 - 11n^4 - 9 $$

Combine like terms

$$
LATEXBLOCK0
$$

Determine degree and number of terms

$$
LATEXBLOCK1
$$

Answer:

• (A) 3rd degree polynomial with 3 terms
• (B) 4th degree polynomial with 4 terms (Correct answer)
• (C) 3rd degree polynomial with 4 terms
• (D) 4th degree polynomial with 3 terms