Mathematics
Find the value of a so that (x + 6) is a factor of the polynomial (x3 + 5x2 - 4x + a).
Factorisation
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Answer
Let f(x) = x3 + 5x2 - 4x + a.
Given,
Factor: x + 6
Thus, on dividing x3 + 5x2 - 4x + a by x + 6, remainder will be zero.
⇒ f(-6) = 0
⇒ (-6)3 + 5(-6)2 - 4(-6) + a = 0
⇒ -216 + 180 + 24 + a = 0
⇒ -12 + a = 0
⇒ a = 12.
Hence, the value of a = 12.
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