Q1 of 82 Page 130

Let us calculate and write, which of the following polynomials will have a factor (x + 1)?

2x3 + 3x2 – 1

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 x + 1


x + 1 = 0


x = – 1


if f(x) is 2x3 + 3x2 – 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 2x3 + 3x2 – 1


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