Sum
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.
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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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