Q2 of 82 Page 130

By using Factor Theorem, let us write whether g(x) is a factor of the following polynomials f(x).

f(x) = 2x3 + 7x2 – 24x – 45 and g(x) = x – 3

Formula used.


If f(x) is a polynomial with degree n


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


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


x – 3 = 0


x = 3


if f(x) is 2x3 + 7x2 – 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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