CAT Quantitative Aptitude Questions | CAT Algebra - Polynomials questions

The question is about Polynomial Remainder Theorem. How you would relate the remainder and the value of polynomial function using polynomial remainder theorem. Polynomials is a simple topic which involves a lot of basic ideas. Make sure that you a get of hold of them by solving these questions. A range of CAT questions can be asked based on this simple concept.

Question 5: What is the remainder when x⁴ + 5x³ – 3x² + 4x + 3 is divided by x + 2?

1. -41
2. -31
3. -18
4. 41

Explanatory Answer

Method of solving this CAT Question from CAT Algebra - Polynomials: This can be solved by substituting all the values in the given equation. As simple as that!!

When f(x) is divided by x-a , the remainder = f(a),
Here f(x) = x⁴ + 5x³ – 3x² + 4x + 3
x + a = x + 2
a = -2
Therefore remainder = f(-2) = (-2)⁴ + 5(-2)³ – 3 (-2)² + 4(-2) + 3
F(-2) = 16 - 40 - 12 - 8 + 3
F(-2) = -41
Hence remainder is -41

The question is "What is the remainder when x⁴ + 5x³ – 3x² + 4x + 3 is divided by x + 2?"

Hence the answer is "-41"

Choice A is the correct answer.