Q1 of 82 Page 130

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

x4 + x3 – x2 + 4x + 5

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 x4 + x3 – x2 + 4x + 5


then putting x = – 1;


f( – 1) = ( – 1)4 + ( – 1)3 – ( – 1)2 + 4( – 1) + 5


= 1 – 1 – 1 – 4 + 5


= 0


Conclusion.


∴ (x + 1) is a factor of x4 + x3 – x2 + 4x + 5


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