What number should be subtracted from 2x 3 - 5x 2 + 5x + 8 so that the resulting polynomial has a factor 2x - 3 ?

Let no. to be subtracted be a. So, resulting polynomial is 2x 3 - 5x 2 + 5x + 8 - a. By factor theorem, A polynomial f(x) has a factor (x - a), if and only if, f(a) = 0. Given, Factor : 2x - 3 = 0 x = Substituting value of x = in 2x 3 - 5x 2 + 5x + 8 - a, will give remainder = 0. Hence, number to be subtracted is 11.