Question

If \( p(x) = 3x^{3} + x^{2} + 2x + 5 \) is divided by \( q(x) = x^{2} + 2x + 1 \), then the degree of the quotient will be:

• A. \(1\)
• B. \(2\)
• C. \(3\)
• D. \(4\)

Hint:

While dividing polynomials, the quotient’s degree is the difference of degrees (provided leading terms don’t cancel).

Answer 1

The Correct Option is A

Step 1: Use degree rule for polynomial division.
For nonzero polynomials, \(\deg(\text{quotient})=\deg(\text{dividend})-\deg(\text{divisor})\) when \(\deg(\text{dividend})\ge\deg(\text{divisor})\).
Step 2: Apply to given polynomials.
\(\deg p=3,\ \deg q=2 \Rightarrow \deg(\text{quotient})=3-2=1.\)