Question

what should be added in the polynomial x³+2x²-9x+1 so that it is completely divisible by x+4

Answer 1

Solution with ans is attached below

Answer 2

Let $f(x)=x^{3}+2 x^{2}+9 x+1$

And, the number to be added be a.

$\therefore f(x)=x^{3}+2 x^{2}+9 x+1+a$

f(x) is to be divided by (x+4).

$\begin{array}{c}{\text { i.e.}\ x=-4} \\ {\Rightarrow(-4)^{3}+2(-4)^{2}+9 (-4)+1+a=0} \\ {\Rightarrow-64+32-36+1+a=0} \\ {\Rightarrow-67+a=0} \\ {\Rightarrow a=67}\end{array}$

Thus, the number to be added is 67.

Polynomial is defined as a combination of x, y, z variables with coefficient, it involves only the operations like addition, subtraction, multiplication, and non-negative integer exponentials  of variables”.