What should be added to the polynomial $x^2-5x+4$, so that 3 is the zero of the resulting polynomial?

Given: $\mathrm{P}\left(\mathrm{x}\right)={\mathrm{x}}^2-5\mathrm{x}+4$

At x = 3,

$\mathrm{P}\left(3\right)=3^2-5\times 3+4$

$\Rightarrow \mathrm{P}\left(3\right)=9-15+4$

$\Rightarrow \mathrm{P}\left(3\right)=-2$

Here, −2 is the remaining number.

Now if we want to make 3 as the zero of the polynomial, we have to add 2 in the given polynomial.

So, to make 3 a zero of the resulting polynomial, you should add 2 to the polynomial, and the resulting polynomial will be:

  ${\mathrm{x}}^2-5\mathrm{x}+4+\mathbf{2}={\mathrm{x}}^2-5\mathrm{x}+6.$