Question

The degree of the polynomial \( (x^5 + x^2 + 3x)(x^6 + x^5 + x^2 + 1) \) is:

• A. \( 5 \)
• B. \( 6 \)
• C. \( 11 \)
• D. \( 10 \)

Hint:

For polynomial multiplication: - The highest degree term determines the overall degree. - The sum of the degrees of individual polynomials gives the final degree.

Answer 1

The Correct Option is C

Step 1: The degree of a polynomial is the highest power of \( x \).
Step 2: Finding degrees:
\[ \text{Degree of } (x^5 + x^2 + 3x) = 5, \quad \text{Degree of } (x^6 + x^5 + x^2 + 1) = 6. \] Step 3: The degree of the product is:
\[ 5 + 6 = 11. \]