Answer :
The value of 'a' for which the polynomial leaves a remainder of 19 when divided by x + 1 is 5. When the polynomial is divided by x + 2, the remainder is 60. Therefore correct option is D
The problem requires finding the value of 'a' that makes the remainder 19 when the polynomial p(x) = x^4 - 2x^3 + 3x^2 - ax + 3a - 7 is divided by x + 1. To find 'a', we apply the remainder theorem by substituting x = -1 into p(x), which results in p(-1) = 19. By solving this equation, we determine a=5.
Subsequently, to find the remainder when p(x) is divided by x + 2, we substitute x = -2 into the polynomial with the new value of 'a'. This computation results in a remainder of 60.
