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Question
Find the value of a such that (x − 4) is a factors of 5x3 − 7x2 − ax − 28.
Solution
Let `f(x) = 5x^3 - 7x^2 - ax - 28` be the given polynomial.
By the factor theorem,
(x − 4) is a factor of f(x).
Therefore f(4) = 0
Hence , `f(4) = 5(4)^2 - 7(4)^2 - a (4) - 28 = 0`
\[\Rightarrow 320 - 112 - 4a - 28 = 0\]
\[ \Rightarrow 180 - 4a = 0\]
\[ \Rightarrow a = \frac{180}{4} = 45\]
Hence, a = 45
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