Answer :

Formula used.

If f(x) is a polynomial with degree n

Then (x – a) is a factor of f(x) if f(a) = 0

1^{st} we find out zero of polynomial g(x)

x – 3 = 0

x = 3

if f(x) is 2x^{3} + 7x^{2} – 24x – 45

then putting x = 3 ;

f(3) = 2(3)^{3} + 7(3)^{2} – 24(3) – 45

= 2 × (27) + 7 × (9) – 24x(3) – 45

= 54 + 63 – 72 – 45

= 0

Conclusion.

∴ g(x) is a factor of f(x)

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