Question

plz solve this tell me how it come​

Answer 1

Know this first : If a be a zero of any polynomial f(x), then it is a certain than (x - a) is a factor of that polynomial.

Solution :

It is given that the polynomial p(x) is divisible by (x - 4),

i.e., (x - 4) is a factor of p(x)

and 2 is a zero of p(x),

i.e., (x - 2) is also a factor of p(x).

We combine both the factors (x - 4) and (x - 2) as (x - 4) (x - 2), which is also a factor of p(x)

= x (x - 2) - 4 (x - 2)

= x² - 2x - 4x + 8

= x² - 6x + 8

Thus, Option (C) is correct.