(c) – \(x\).
f(x) = x19 + x17 + x13 + x11 + x7 + x5 + x3
Putting x2 = – 1, we get
f(x) = (x2)9.\(x\) + (x2)8.\(x\) + (x2)6.\(x\) + (x2)5.\(x\) + (x2)2.\(x\) + x2.\(x\)
= (–1)9\(x\) + (–1)8.\(x\) + (–1)6.x + (–1)5.\(x\) + (–1)2.\(x\) + (–1).\(x\)
= – \(x\) + \(x\) + \(x\) – \(x\) + \(x\) – \(x\) = – \(x\).