What is the highest degree for the expression (3x^2 + 4)(x^5−3)−12x^9−24x^3? A) 7 B) 8 C) 9 D) 10

Answer 1

To determine the highest degree of the given expression \((3x^2 + 4)(x^5−3)−12x^9−24x^3\), we need to analyze each component.

1. Degree of \((3x^2 + 4)(x^5 - 3)\):

   • The degree of \(3x^2 + 4\) is 2 (highest power is \(x^2\)).
   • The degree of \(x^5 - 3\) is 5 (highest power is \(x^5\)).
   • When you multiply two polynomials, the degree of the product is the sum of the degrees of the individual polynomials.
   • Therefore, the degree of \((3x^2 + 4)(x^5 - 3)\) is \(2 + 5 = 7\).

2. Degree of \(-12x^9\):

   • The degree is 9.

3. Degree of \(-24x^3\):

   • The degree is 3.

Now, we combine the results:

• The degree of \((3x^2 + 4)(x^5 - 3)\) is 7.
• The degree of \(-12x^9\) is 9.
• The degree of \(-24x^3\) is 3.

Next, we find the highest degree among these:

• The degrees we have are 7, 9, and 3.
• The highest degree is \(9\) from the term \(-12x^9\).

Thus, the highest degree of the entire expression \((3x^2 + 4)(x^5 - 3) - 12x^9 - 24x^3\) is \(9\).

The answer is \(C) 9\).