Question

Find 'a' if the two polynomials ax^3+3x^2-9 and 2x^3+4x+a ,leaves the same remainder when divided by x+3

Answer 1

gives same remainder when are divide by x+3
hence put x=-3...and equate equations
$a( - 3) {}^{3} + 3( - 3) {}^{2} - 9 = 2( - 3) {}^{3} + 4( - 3) + a \\ - 27a + 27 - 9 = - 54 - 12 + a \\ - 28a = - 66 + 9 - 27 \\ - 28a = - 66 - 18 \\ a = 3$
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Answer 2

When we divide 2x^3+4x+a by x+3
We get the remainder a-66
Then when we divide ax^3+3x^2-9 by x+3 we obtain 18- 27a as the remainder.
As we know that both obtain the same remainder a - 66= 18-27a
then by solving the above we will get a=3