Question

if polynomial ax3 + 3x2 - 3 and 2x3 - 5x + a leaves the same remainder when each is devided by x - 4 find the valuse of a

Answer 1

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