Question

Find the value of a, if the polynomial is ax^3+3x^2-3 and 2x^3-5x+a , when divided by x-4 , leaves the same remainder.

Answer 1

Answer: 1

Step-by-step explanation:

P(x) = ax^3+3x^2-3

P(4) = a×4^3+3×4^2-3

= 64a + 45

P(x) = 2x^3- 5x + a

P(4) = 2×4^3-5×4 +a

=128 - 20 + a

= 108 + a

Since they leaves the same remainder,

64a + 45 = 108 + a

64a- a = 108 -45

63 a = 63

a = 63/63 = 1