Q. 4 C3.6( 5 Votes )

# Let us calculate the value of k for which g(x) will be a factor of the following polynomials f(x).f(x) = 2x4 + x3 – kx2 – x + 6 and g(x) = 2x – 3

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)

2x – 3 = 0

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

then f( ) = 0 ;

f( ) = 2( )4 + 3 – k( )2 + 6 = 0

= = = = = 0

144 – 18k = 0

k = = 8

Conclusion.

if (2x – 3) is factor of f(x) then k = 8

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