Question

The polynomials ax³ + 3x² – 3 and 2x³ – 5x + a, when divided by x – 4, leave the same remainder in each case. Find the value of a. 

Answer 1

let f(x)` (ax^3+3x^2-3) `

when f (x) is dividend by(x-4), remainder =f(4) 

f(4)=`a(4)^3+3(4)^2-3=64a+45 `

let `g (x)=2x^3-5x+a `

When g (x) is divided by (x-4), remainder =g(4) 

`g(4)=2(4)^3-5(4)+=a+108  `

it is given that` f(4)=9(4) `

`64a+45=a+108 `

`63a=63 `

`a=1`