Question

Find 'a' if the polynomials ax3 + 3x2 – 9 and 2x3 + 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

\begin{lgathered}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\end{lgathered}

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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