Question

by remainder theorm find the remaindrr when p(x)=4xcube-3x ssquar+2x-5is divided by g(x)=1-2x. if y-1 is the factor of kycube +y square +2y -4k-10,then find the value of k

Answer 1

p(x) = 4x^3 - 3x^2 + 2x - 5
zero of g(x) = 1 - 2x
1 - 2x = 0
-2x = -1
x = 1/2
Now, remainder when p(x) is divided by g(x)

P(1/-2) = 4(1/2)^3 - 3(1/-2)^2 + 2(1/2) - 5
1/2 - 3/4 + 1 - 5
2-3/4 - 4
-1/4-4
-1+16/4
-17/4 is the remainder.

Now, 2nd part
zero of y-1 = 1
if y-1 is the is the factor of p(y) then
p(1) = 0
Therefore
k(1)^3 + (1)^2 + 2(1) - 4k - 10 = 0
k + 1 + 2 - 4k - 10 = 0
-3k - 7 = 0
-3k = 7
k = -7/3

Hole this will help you