Find a and b such that (x+1) and (x+2) are factors of polynomial x^3 +ax^2 -bx+ 10.

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Solution

Let p(x) = x3 + ax2 -bx+10

x+1 is a factor of p(x), so p(-1) = 0
-1 + a + b + 10 = 0 or a + b + 9 = 0 ... (1)

x+2 is a factor of p(x), so p(-2) = 0
-8 + 4a + 2b + 10 = 0 or 2a + b + 1 = 0 ... (2)

Solve equations (1) and (2) to get the required values of a and b.

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