Q1 of 82 Page 130

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

3 + 3x – 5x3 – 5x4

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 3 + 3x – 5x3 – 5x4


then putting x = – 1;


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


= 3 + 3 × ( – 1) – 5 × ( – 1) – 5 × 1


= 3 – 3 + 5 – 5


= 0


Conclusion.


∴ (x + 1) is a factor of 3 + 3x – 5x3 – 5x4


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