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# 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. - Mathematics

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#### 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.

#### 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

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