Answer to Question #69214 in Calculus for srinvasa rao

Question

1. The polynomials ax^3+3x^2−13 and 2x^3 - 5x + a are divided by (x+2). If the remainder in each case is the same, find the value of a.

2. What must be subtracted from 4x^4 - 2x^3 - 6x^2 + x - 5 so that the result is exactly divisible by 2x^2 + x - 1? Use long division method.

3. What must be added to x^4 + 2x^3 - 2x^2 + x - 1 so that the result is exactly divisible by
x^2 + 2x - 3 ? Use long division method.

4. If a+b=1, then prove that a^3 + b^3 + 3ab = 1.

5. Factorise:
a) 2√2a^3 + 16√2b^3 + c^3 − 12abc
b) 2√2x^3 + 3√3y^3 + √5(5−5√6xy)

6. Factorise: a / b x^2 + (a / b + c / d)x + c / d; { b not equal to 0, d = 0 }

7. Factorise: (ax - by)^3 + (by - cz)^3 + (cz - ax)^3