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 x + 1

x + 1 = 0

x = – 1

if f(x) is 2x^{3} + 3x^{2} – 1

then putting x = – 1;

f( – 1) = 2( – 1)^{3} + 3( – 1)^{2} – 1

= 2 × ( – 1) + 3 × (1) – 1

= – 2 + 3 – 1

= 0

Conclusion.

∴ (x + 1) is a factor of 2x^{3} + 3x^{2} – 1

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