Q. 2 B4.7( 3 Votes )
By using Factor Theorem, let us write whether g(x) is a factor of the following polynomials f(x).
f(x) = 2x3 + 9x2 – 11x – 30 and g(x) = x + 5
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
1st we find out zero of polynomial g(x)
x + 5 = 0
x = – 5
if f(x) is 2x3 + 9x2 – 11x – 30
then putting x = – 5 ;
f( – 5) = 2( – 5)3 + 9( – 5)2 – 11( – 5) – 30
= 2 × ( – 125) + 9 × (25) – 11x( – 5) – 30
= – 250 + 225 + 55 – 30
= 0
Conclusion.
∴ g(x) is a factor of f(x)
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