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If remainder is same when polynomial p(x)=x3+8x2+17x+ax is divided by x+2 and x+1.find the value of a.
When p(x)=x 3 +8x 2 +17x+ax is divided by (x+2) & (x+1) we get the same remainder.

Therefore, p(-2) = p(-1)

? (-2) 3 + 8(-2) 2 +17(-2) + a(-2) = (-1) 3 +8(-1) 2 +17(-1) + a(-1)

? -8 + 32 -34 -2a = -1+ 8 -17 - a

? -10 -2a = -10 - a

? -2a = - a

? -2a + a = 0

? a = 0

Hence, for a = 0, the polynomial p(x) on division by (x + 2) and (x + 1) will give the same remainder.


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