Using factor theorem, show that g(x) is a factor of p(x), when
p(x)=2x3+7x2−24x−45,g(x)=x−3
Let:
p(x)=2x3+7x2−24x−45g(x)=x−3x=3
By the factor theorem, (x - 3) is a factor of the given polynomial if p(3) = 0.
Thus, we have:
p(2)=2×33−7×32−24×3−45=54+63−72−45=0
Hence, (x - 3) is a factor of the given polynomial.