Question

find the value of a from which polynomial
$(x ^{2} - x ^{3} - 11x + a)$
is divisible by
$(x + 3)$

Answer 1

When divided by x+3, the polynomial x2-x3-11x+a is completely divisible.. so, remainder is zero


so, when you substitute x+ 3= 0 (or) x= - 3, you will get the remainder which is zero

substituting x= -3 in x2-x3-11x+a =0, we get


(-3)^2 - (-3)^3 - 11(-3) + a =0

9 - (-27) + 33 + a =0

9 + 27 + 33+ a= 0

so, a = -69 is the required answer

Answer 2

As u can can se in the attachment, when I divided x²-x³-11x by x+3 it leaves a remainer which is equal to -3

That means we have to add (3) to make it completely divisible by x+3
so a= 3