CAT Quantitative Aptitude Questions | CAT Algebra - Polynomials questions

The question is about 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 7: 4x³ + ax² – bx + 3 divided by x – 2 leaves remainder 2, divided by x + 3 leaves remainder 3. Find remainder when it is divided by x + 2.

1. 26.8
2. 29.2
3. 32.2
4. 35.2

Video Explanation

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!!

Let f(x) = 4x³ + ax² – bx + 3.
Remainder on division of f(x) by x - 2 = f(2)
Or, f(2) = 32 + 4a – 2b + 3 = 2
4a – 2b = -33 ---- (1)
Remainder on division of f(x) by x + 3 = f(-3)
Or, f(-3) = –108 + 9a + 3b + 3 = 3
9a + 3b = 108
Dividing by 3, the above equation becomes
3a + b = 36. Multiplying this equation by 2, we get
6a + 2b = 72 ---- (2)
Adding equations (1) and (2), we have 10a = 39
a = 3.9
4(3.9) – 2b = –33
b = 24.3
f(x) = 4x³ + 3.9x² – 24.3x + 3
Remainder on division of f(x) by x + 2 = f(-2)
f(–2) = 4(–8) + 3.9(4) – 24.3(–2) + 3 = 35.2

The question is "4x³ + ax² – bx + 3 divided by x – 2 leaves remainder 2, divided by x + 3 leaves remainder 3. Find remainder when it is divided by x + 2."

Hence the answer is "35.2"

Choice D is the correct answer.