Find the value of my for which (2x-1) is a factor of 8x^4 + 4x^3 - 16x

1.	Find the value of my for which (2x-1) is a factor of 8x^4 + 4x^3 - 16x^2 + 10x + m
Answer» <P>Let p(X)=8x 4 +4x 3 −16x 2 +10x+m and g(x)=2x−1 Now, g(x)=2x−1 =>2x−1=0 =>x= 2 1 If g(x) is a FACTOR of p(x), then p( 2 1 ) must be 0 Thus, p( 2 1 )=0 =>8( 2 1 ) 4 +4( 2 1 ) 3 −16( 2 1 ) 2 +10( 2 1 )+m=0 => 16 8 + 8 4 − 4 16 +5+m=0 => 2 1 + 2 1 −4+5+m=0 =>1+1+m=0 =>m=−2

Find the value of my for which (2x-1) is a factor of 8x^4 + 4x^3 - 16x^2 + 10x + m

Answer»

<P>Let p(X)=8x

+4x

−16x

+10x+m and g(x)=2x−1

Now, g(x)=2x−1

=>2x−1=0

=>x=

If g(x) is a FACTOR of p(x), then p(

) must be 0

Thus, p(

)=0

=>8(

)

+4(

)

−16(

)

+10(

)+m=0

−

+5+m=0

−4+5+m=0

=>1+1+m=0

=>m=−2