Question

14. Find the value of ‘k’ for which the polynomial x 4

+10x3

+25x2

+15x+k is exactly divisible by (x+7)

Answer 1

x+7 is a factor then
x+7=0
x=-7
P(x)=x4+10x3+25x2+15x+k
Putting the value of x in the equation
P(-7)= (-7)4+10(-7)3+25(-7)2+15(-7)+k
The whole equation will be equal to 0 as -7 is a factor
P(-7)= -28+(-3430)+725+(-105)+k=0
P(-7)=-28-3430+725-105+k=0
P(-7)=725-3563+k=0
P(-7)=-2838+k=0
P(-7)=k=2838
That's your answer

Answer 2

Hope it helps............