Find the value of a such that (x-4) is a factor of 5x3-7x2-ax-28.
Let f(x) = 5x3-7x2-ax-28 be the given polynomial.
From factor theorem,
If (x -4) is a factor of f (x) then f (4) = 0
f (4) = 0
0 = 5 (4)3 – 7 (4)2 – a (4) – 28
0 = 320 – 112 – 4a – 28
0 = 180 – 4a
4a = 180
a = 45
Hence, (x – 4) is a factor of f (x) when a = 45.