Mathematics
While factorizing a given polynomial, using remainder and factor theorem, a student finds that x + 3 is a factor of 2x3 - x2 - 5x - 2.
(a) Is the student's, solution correct stating that (x + 3) is a factor of the given polynomial?
(b) Give a valid reason for your answer.
(c) Factorize the given polynomial completely.
Related Questions
When the polynomial x3 + 2x2 - 5ax - 7 is divided by (x - 1), the remainder is A and when the polynomial x3 + ax2 - 12x + 16 is divided by (x + 2), the remainder is B. Find the value of 'a' if 2A + B = 0.
(3x + 5) is a factor of the polynomial (a - 1)x3 + (a + 1)x2 - (2a + 1)x - 15. Find the value of 'a'. For this value of 'a', factorise the given polynomial completely.
Using remainder theorem, find the value of k if on dividing 2x3 + 3x2 - kx + 5 by (x - 2) leaves a remainder 7.
Find the value of 'a' if x - a is a factor of the polynomial 3x3 + x2 - ax - 81.