For what value of a is (x-5) a factor of x3-3x2+ax-10.
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 – 75 + 5a – 10
0 = 5a + 40
a = -8
Hence, (x – 5) is a factor of f (x), if a = - 8.