Question

Find the value of k, for which polynomial p(x) is
exactly divisible by polynomial g(x), in each of the
following:
(1) p(x) = x + 8x² + kx + 18, g(x) = x2 + 6x+9​

Answer 1

Step-by-step explanation:

g(x) = x2 + 6x+9=0

g(x) = x^2+ 3x +3x +9=0

g(x) =x(x+3) +3(x+3)=0

g(x) =(x+3) (x+3)=0

g(x)= (x+3)=0

g(x)=x=-3

p(x) = x + 8x² + kx + 18=0

P(x) =(-3)+8(-3)^2 +(-3)k +18=0

P(x)=-3 +72-3k+18=0

P(x) =87 - 3k =0

P(x) =-3k =-87

P(x)= k=-87/-3

P(x)= k=29

Hence polynomial p(x) is not

exactly divisible by polynomial g(x)...