Factor Theorem-5

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Find the value of a if x + a is a factor of the polynomial x3 + ax2 - 2x + a + 4.

Solution: Let f(x) = x3 + ax2 - 2x + a + 4

(x + a) is a factor of f(x) if f( -a) = 0

f( -a) = ( -a)3 + a.( -a)2 - 2( -a) + a + 4

= - a3 + a3 + 2a + a + 4 = 3a + 4

f( -a) = 0

=> 3a + 4 = 0

=> a = - 4/3

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