If the polynomials `a x^3+3x^2-13` and `2x^3-5x+a ,` when divided by `(x-2)` leave the same remainder, find the value of `a` .

Explanation

"""Solution,
Given polynomial `p(x) = ax³ + 3x² - 13 and 2x² - 5x + a` is divided by `x-2` get
same remainder
Then `x-2=0` or `x=2`
`p(x) = ax³ + 3x^2-13`
Replace `x` by `2` we get
`p(2)= a(2)³ +3(2)² - 13`
`p(2)= 8a+ 12-13`
⇒`p(2) = 8a-1`
`2x²-5x + a`
Replace `x` by `2` we get
`q(2) = 2(2)³ - 5(2) + a`
⇒`q(2)=16-10+ a`
⇒`q(2) = 6+ a`
Given remainder is same
`:.8a=1=6+a`

`8a-1+1-a=6+a+1-a`
⇒ `7a = 7`⇒ `a = 1`"""