Answer:
a = 3
Step-by-step explanation:
[tex]p(x) = 2x^{3} + ax^{2} +3x -3\\f(x) = x^{3} + x^{2} - 4x + a[/tex]
To get the remainder when these polynomials are divided by x - 2, subsitute(x = 2) into both functions.
[tex]p(2) = 2(2^{3}) + a(2^{2}) +(3*2) -3\\p(2) = 19 - 4a\\f(2) = 2^{3} + 2^{2} - (4*2) + a\\f(2) = 4 + a[/tex]
Since the remainders are the same, p(2) = f(2)
19 - 4a = 4 + a
19 - 4 = a + 4a
15 = 5a
a = 15/5
a = 3
