Question

The number to be added to the polynomial x$x^{2}-5x+4$ so that 3 is the zero of the polynomial .

Answer 1

As 3 should be the zero, substitute 3 in place of x. while assuming alpha as tje number to be added. $\Therefore \ 9-45+4+\alpha=0\implies \; \alpha=45-13\; \implies \alpha=32$
So the answer is 32.

Answer 2

Let number P is added to the polynomial x² - 5x + 4 so that 3 is the zero of the polynomial .

now, put 3 in polynomial x² - 5x + 4 + P
(3)² - 5(3) + 4 + P = 0
9 - 15 + 4 + P = 0
P = 2

then, x² - 5x + 4 + 2 = x² - 5x + 6
= (x - 2)(x - 3)