Question

Find teh number which should be added to $x^2+x+3$ so that the resulting polynomial is completely divisible by (x+3).

Answer 1

Let the required number be k.
Let f(x) = $x^2+x+3+k$
It is given that f(x) is divisible by (x + 3).
Remainder = 0
f (-3) = 0
${(-3)}^2$ + (-3) + 3 + k = 0
9 – 3 + 3 + k = 0
9 + k = 0
k = -9
Thus, the required number is -9.