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) = 2x^{3} + 9x^{2} – 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

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

x + 5 = 0

x = – 5

if f(x) is 2x^{3} + 9x^{2} – 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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