Sum

The polynomials ax^{3} + 3x^{2} – 3 and 2x^{3} – 5x + a, when divided by x – 4, leave the same remainder in each case. Find the value of a.

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#### Solution

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`

Concept: Remainder Theorem

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