# CAT Quantitative Aptitude Questions | CAT Algebra - Polynomials questions

###### CAT Questions | Algebra | Polynomials - Polynomial Remainder Theorem CAT Questions

The question is about Polynomial Remainder Theorem. This can be solved by substituting all the values in the given equation. As simple as that!! 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 3: x4 – ax3 + bx2 – cx + 8 = 0 divided by x – 1 leaves a remainder of 4, divided by x + 1 leaves remainder 3, find b.

1. 2.5
2. -5.5
3. 3.5
4. 6.5

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##### 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) = x4 – ax3 + bx2 – cx + 8

f(1) = 4
1 – a + b – c + 8 = 4
–a + b – c = - 5 ...... Eqn (1)
f(–1) = 3
1 + a + b + c + 8 = 3
a + b + c = - 6 ...... Eqn (2)
Adding Equation (1) and (2) we have
2b = -11,
or b = -5.5

The question is "x4 – ax3 + bx2 – cx + 8 = 0 divided by x – 1 leaves a remainder of 4, divided by x + 1 leaves remainder 3, find b."

##### Hence the answer is "-5.5"

Choice B is the correct answer.

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