Question

find the value of a for which the polynomia x⁴ -x³ -11x² -x + a is divisible by x+ 3

Answer 1

solution.

Here Polynomial is devided by x+ 3

so,x+ 3 is factor

so, x= -3

Now, putting the value of x in Polynomial.

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

=> -27 - 99 + 3+a= 0

=> -123+ a

=> a= 123

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hope it helps☺✌✌

Answer 2

given ,
f(x)=x⁴-x³-11x²-x+a
g(x)=x+3
compairing x+3 with x-a 
a=-3
 now , for the f(x) to be exactly divisible by x+3
f(a)=0
or,(-3)⁴-(-3)³-11*(-3)²-(-3)+a =0
or,81-27-99+3+a=0
or,-42+a=0
or,a=42
so the required value of a is 42.