The polynomials `a x^3+3x^2-13` and `2x^3-5x+a` are divided by `x+2,` if the remainder in each case is the same, find the value of `adot`

Explanation

Solution`p(x) = ax³ + 3x² - 13` and `q(x) = 2x³ – 5x + a`
When `p(x)` and `q(x)` are divided by `x+2=0⇒x=-2`
`p(-2)=q(-2)`= `a(-2)^3 + 3(-2)^2-13=2(-2)³-5(-2) + a`
⇒`-8a+12-13=-16+ 10+ a`
⇒`9a = -5⇒a= 5/9`