Question

when the polynomial kx3+9x3+4x-8 is divided by x+3 then a remainder 7 is obtained. find the value of k

Answer 1

Let p(x)=kx^3+9x^3+4x-8
According to remainder theorem after dividing p(x) by x+3
We will get p(-3) as remainder

So,
p(-3)=k(-3)^3+9(-3)^3+4(-3)-8
p(-3)=-27k-243-12-8
p(-3)-27k-263


but remainder=7

-27k-263=7
-27k=7+263
-27k=270
-k=270/27
-k=10
k=-10