Answer:
a = 1
Step-by-step explanation:
Given that both ax³ + 3x² - 3 and 2x³ - 5x + a have the same remainder when divided by x - 4.
x - 4 = 0
x = 4
When ax³ + 3x² - 3 is divided by x - 4, the remainder is gotten by substituting x = 4:
a(4)³+3(4)²-3 = 64a + 48 - 3 = 64a + 45
The remainder is 64a³ + 45
For 2x³ - 5x + a we find the remainder by substituting x = 4:
2(4)³ - 5(4) + a = 128 - 20 + a = 108 + a
Since they both have the same remainder, therefore:
64a + 45 = 108 + a
64a - a = 108 - 45
63a = 63
a = 1
