Question

If \(p(x) = x^4 - 2x^3 + 17x^2 - 4x + 30\) is divided by \(q(x) = x + 2\) then the degree of the quotient is

• A. 6
• B. 3
• C. 4
• D. 5

Hint:

This rule is very useful for quickly determining the nature of the result of polynomial division without carrying out the lengthy process.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
When a polynomial is divided by another polynomial, the degree of the quotient (the result of the division) can be determined by subtracting the degree of the divisor from the degree of the dividend.

Step 2: Key Formula or Approach:
Degree of Quotient = Degree of Dividend - Degree of Divisor

Step 3: Detailed Explanation:
The dividend is \(p(x) = x^4 - 2x^3 + 17x^2 - 4x + 30\).
The degree of a polynomial is the highest power of the variable.
The degree of the dividend \(p(x)\) is 4.
The divisor is \(q(x) = x + 2\).
The degree of the divisor \(q(x)\) is 1.
Now, apply the formula:
\[ \text{Degree of Quotient} = 4 - 1 = 3 \] We do not need to perform the actual division.

Step 4: Final Answer:
The degree of the quotient is 3.