Using factor theorem, show that g(x) is a factor of p(x), when
p(x)=7x2−4√2x−6,g(x)=x−√2
p(x)=7x2−4√2x−6g(x)=x−√2x=√2
If p(x) is a multiple of g(x), the remainder will be zero.
p(√2)=7(√2)2−4√2(√2)−6=14−8−6=0
Therefore p(x) is a multiple of g(x)