Q3 of 82 Page 130

Let us calculate and write the value of k for which the polynomial 2x4 + 3x3 + 2kx2 + 3x + 6 is divided by x + 2.

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 + 2 = 0


x = – 2


if x + 2 is factor of f(x) = 2x4 + 3x3 + 2kx2 + 3x + 6


then f( – 2) = 0 ;


f( – 2) = 2( – 2)4 + 3( – 2)3 + 2k( – 2)2 + 3( – 2) + 6 = 0


= 2 × 16 – 3 × 8 + 8 × k – 6 + 6


= 32 – 24 + 8k – 6 + 6


8 + 8k = 0


8k = – 8


k = = – 1


Conclusion.


∴ if (x + 2) is factor of f(x) then k = – 1


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