For what value of a is (x-5) of factor of x³-3x²+ax-10.
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i am very poor in maths...........
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Step-by-step explanation:
Let, f (x) = x³ - 3x² + ax - 10 be the given polynomial.
By factor theorem, If (x – 5) is a factor of f (x) then f (5) = 0 :
Now,
f (x) = x³ - 3x² + ax - 10
=> f (5) = (5)³– 3 (5)² + a (5) – 10
=> 0 = 125 - 3 × 25 + 5a - 10
=> 0 = 125 – 75 + 5a – 10
=> 0 = 5a + 40
=> -5a = 40
=> a = - 40/5
=> a = - 8
Hence, (x – 5) is a factor of f (x), if a = - 8.
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