If a is defined by f (x)=a(0)x^(n)+a(1)x...

If a is defined by f `(x)=a_(0)x^(n)+a_(1)x^(n-2)+a_(2)x^(n-2)+...+a_(n-1)x+a_(n)` where n is a non negative integer and `a_(0),a_(1),a_(2),…….,a_(n)` are real numbers and `a_(0) ne 0,` then f is called a polynomial function of degree n. For polynomials we can define the following theorem
(i) Remainder theorem: Let p(x) be any polynomial of degree greater than or equal to one and 'a' be a real number. if p(x) is divided by (x-a), then the remainder is equal to p(a).
(ii) Factor theorem : Let p(x) be a polynomial of degree greater than or equal to 1 and 'a' be a real number such that p(a) = 0, then (x-a) is a factor of p(x). Conversely, if (x-a) is a factor of p(x). then p(a)=0.
The factor of the polynomial `x^(3)+3x^(2)+4x+12` is

`x+3`

`x-3`

`x+2`

`x-2`

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