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Question
Find ‘a‘ if the two polynomials ax3 + 3x2 – 9 and 2x3 + 4x + a, leave the same remainder when divided by x + 3.
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Solution
`x+3=0` ⇒ `x=-3`
Since, the given polynomials leave the same remainder when dividend by (x-3),
value of polynomial `ax^3+3x^2-9` at x=-3 is sae as value of polynomial `2x^3+4x+a at x=-3`
⇒ `a(-3)^3+3(-3)^2-9=2(-3)^3+4(-3)++a`
⇒`-27a+27-9=-54-12+a`
⇒`-27a+18=-66+a`
⇒`28a=84`
⇒`a=84/28`
⇒a=3
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