Question

what must be subtracted from p(x) = 4x^4-2x^3-6x^2+x-5 so that the result is exactly divisible by 4x^2 +2x. Answer briefly pls.

Answer 1

Answer:

4x^2+2x=0

4x^2= -2x

x^2= -2x/4

x^2= -1x/2

x^2/x= -1/2

Step-by-step explanation

taking the x to the left hand side

therefore x= -1/2

now,P(x)=4x^4-2x^3-6x^2+x-5

substitute x value in the equation

let the no. needed to be subtracted  be Y

if 4x^2+2x is a factor of the given equation the remainder should be 0

therefore

P(-1/2) =0

p(-1/2)=4*(-1/2)^4-2*(-1/2)^3-6*(-1/2)^2+(-1/2)-5-Y

0=4*(1/16)-2*(-1/8)-6*(1/4)-(1/2)-5-Y

0=(1/4)+(1/4)-(3/2)-(1/2)-5-Y

0=(1+1-6-2-20-4Y)/4

TAKING 4 AS THE L.C.M

0=-26-4Y

4Y=-26

Y= -6.5

HOPE THIS HELPS AND IS RIGHT