Q4 of 82 Page 130

Let us calculate the value of k for which g(x) will be a factor of the following polynomials f(x).

f(x) = 2x3 + 9x2 + x + k and g(x) = x – 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 g(x)


x – 1 = 0


x = 1


if x – 1 is factor of f(x) = 2x3 + 9x2 + x + k


then f(1) = 0 ;


f(1) = 2(1)3 + 9(1)2 + 1 + k = 0


= 2 + 9 + 1 + k


12 + k = 0


k = – 12


Conclusion.


∴ if (x – 1) is factor of f(x) then k = – 12


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