Problems on algebra-III





                   In this page 'Problems on algebra-III' we are going to see problems based on remainder theorem.

                   Parents and teachers can guide the students to do the problems on their own. If they are having any doubt they can verify the solutions.

                  Before going to the problems let us see about "Remainder theorem".

                                    Remainder theorem

                      Let p(x) be any polynomial and a be any real number.  If p(x) is divided by the linear polynomial x-a, then the remainder is p(a).

Note:

  1. If p(x) is divided by (x+a), then the remainder is p(-a).
  2. If p(x) is divided by (ax-b), then the remainder is p(b/a).
  3. If p(x) is divided by (ax+b), then the remainder is p(-b/a).
  4. Here -a, b/a, and -b/a are the zeros of the divisors x+a, ax-b and ax+b respectively.


Problems on algebra-III

1.       Find the remainder using remainder theorem, when

         (i)      3x³ + 4x² - 5x +8 is divided by x-1.

           (ii)        5x³ + 2x² - 6x +12 is divided by x+2.

           (iii)        2x³ - 4x² + 7x +6 is divided by x-2.

           (iv)        4x³ -3x² + 2x -4 is divided by x+3

            (v)        4x³ - 12x² +11x -5 is divided by 2x-1   

            (vi)       8x  + 12x³ -2x² - 18x +14 is divided by x+1

  .         (vii)       x³   -  ax²  - 5x  +2a is divided by x-a.


2.         When the polynomial 2x³ - ax² + 9x -8 is divided by x-3 the remainder is 28.   Find the value of a.

3.         Find the value of m if x³ - 6x² +mx + 60 leaves the remainder 2 when divided by (x+2).

4.         If (x-1) divides mx³ -2x² + 25x - 26 without remainder find the value of m.

5.         If the polynomials x³ + 3x² -m and 2x³ -mx + 9 leave the same remainder when they are divided by (x-2), find the value of m. Also find the remainder.


                                        Solutions

                         Students can try to solve the problems on their own. Parents and teachers can encourage the students to do so. If they are having any doubt they can verify the solutions.  If you are having any further doubt you can contact us through mail, we will help you to clear your doubt.





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